I 


1 


PLATE  XV/. 


ESSAY, 

ON  THE  USE  OF  THK 

Celestial  anti  Xemstrial 

GLOBES; 

EXEMPLIFIED  IN  A  GREATER  VARIETY  OF  PROBLEMS,  THAN  ARE 
TO  BE  FOUND  IN  ANY  OTHER  WORK ; 

Exhibiting  the  general  Principles  of 

DIALING  AND  NAVIGATION. 


BY  THE  LATE 

GEORGE  ADAMS, 

Mathematical  Instrument  Maker  to  His  Majesty,  and  Optician  to  the  Prince  of  Wales. 


FIFTH  EDITION, \ 

WITH  THE  AUTHOR’S  LAST  IMPROVEMENTS, 
Illustrated  with  Copper  Plates. 


PHILADELPHIA: 

PUBLISHED  BY  WILLIAM  W.  WOODWARD, 
No.  52,  South  Second  Street. 

1808. 

Dickinson.  Printer. 


I 


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Digitized  by  the  Internet  Archive 
in  2018  with  funding  from 
University  of  North  Caro+ina  at  Chapel  Hill 


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https://archive.org/details/essayonuseofceleOOadam 


K 


CONTENTS. 


(  ^  '  \ 

?age> 

OF  the  Use  of  the  Globes  9 

Advantages  of  Globes.  -  -  -  -  9 

Description  of  the  Globes  -  -  -  -  18 

Of  the  Terrestrial  Globe  28 

Of  Latitude  and  Longitude  -  -  -  -  28 


Problem. 

1.  To  find  the  Longitude  of  any  Place 

2.  To  find  the  difference  of  Longitude  between  any 


two  Places  ------  35 

3.  To  find  those  places  where  it  is  Noon  at  any  , 

given  Hour  of  the  Day,  at  any  given  Place  36 

4.  When  it  is  Noon  at  any  Place,  to  find  what 

Hour  it  is  at  any  other  Place  -  -  -  37 

5.  At  any  given  Hour  where  you  are,  to  find  the 

Hour  at  a  Place  proposed  -  -  -  -  38 

Of  Latitude  -------  39 

6.  To  find  the  Latitude  of  any  Place  -  -  -  41 

7.  To  find  all  those  Places  which  have  the  same 

Latitude  with  any  given  Places  -  -  -  41 

8.  To  find  the  Difference  of  Latitude  between  any 

two  Places  ------  42 


IV 


CONTENTS. 


I 


Problem, 


Page. 


9.  The  Latitude  and  Longitude  being  known,  to  find 
the  Place  ------- 

Of  finding  the  Longitude  - 

10.  To  find  the  Distance  of  one  Place  from  another 

11.  To  find  the  Angle  of  Position  of  Places  - 

0 

12.  To  find  the  Bearings  of  Places  -  -  - 

Of  the  twilight  ------ 

To  rectify  the  Globe 

13.  To  rectify  for  the  Summer  Solstice 

14.  - for  the  Winter  Solstice  - 

15.  - for  the  Times  of  Equinox  - 

i  6.  To  exemplify  the  Sun’s  Altitude  - 

17.  Of  the  Sun’s  Meridian  Altitude  - 

18.  To  find  the  Sun’s  Meridian  Altitude  universally 

19.  Of  the  Sun’s  Azimuths  .... 

Of  the  Zones  and  Climates  -  - 

20.  To  find  the  Climates  - 

21.  To  illustrate  the  Distinction  of  Ascii,  Sec. 

22.  To  find  the  Antceci,  See.  - 

23.  To  find  those  Places  over  which  the  Sun  is  verti- 


42 

43 

53 

54 
54 
45 
59 
61 

63 

64 

67 

68 

69 

70 
72 
74 
78 
81 


cial  . -82 

24.  To  find  the  Sun’s  Place  -  -  -  -  83 

25.  To  find  the  Sun’s  Declination  -  -  -  86 

26.  To  find  the  two  Days  on  which  the  Sun  is  in  the 

Zenith  of  any  given  Place,  Sec.  -  -  -  87 

27.  To  find  where  the  Sun  is  vertical  on  a  given  Day 

and  Hour  -  -  -  -  _  -  87 

28.  At  a  given  Time  of  the  Day  in  one  Place,  to  find  at 

the  same  Instant  those  Places  where  the  Sun  is 

rising,  setting,  Sec. . 88 

39.  To  find  all  those  Places  within  the  Polar  Circles, 

on  which  the  Sun  begins  to  shine,  Sec.  -  -  90~ 

■->().  To  make  Use  of  the  Globe  as  a  Tellurian  -  -  91 

-'1.  Io  rectify  the  Globe  to  the  Latitude  and  Horizon 

of  any  Place  - . 95 

j2.  I o  rectify  for  the  Sun’s  Place  -  -  95 


CONTENTS. 


V 


Problem. 

33  To  rectify  for  the  Zenith  of  any  Place 
Of  exposing  the  Globe  to  the  Sun  - 

34.  To  observe  the  Sun’s  Altitude  - 

35.  To  place  the  Globe,  when  exposed  to  the  Sun, 

that  it  may  represent  the  natural  Positions  of 
the  Earth  - 

36.  To  find  naturally  the  Sun’s  Declination 

37.  To  find  naturally  the  Sun’s  Azimuth 

38.  To  shew  where  the  Sun  will  be  twice  on  the 

same  Azimuth  in  the  Morning,  and  twice  in 
the  Afternoon  ------ 

To  find  the  Hour  by  the  Sun  - 

Of  Dialling  ------- 

40.  To  construct  an  Horizontal  Dial  - 

41.  To  delineate  a  South  Dial  - 

42.  To  make  an  erect  Dial  - 

Of  Navigation  - 

43.  Given  the  Difference  of  Latitude,  and  Difference 

of  Longitude,  to  find  the  Course  and  Distance 
sailed  ------- 

c  - 

44.  Given  the  Difference  of  Latitude  and  Course,  to 

find  the  Difference  of  Longitude  and  Distance 


Page. 

96 

97 
100 


102 

104 

105 


106 

108 

112 

117 

121 

122 

126 


"9 

o 


sailed  -  -  -  -  -  -  -133 

45.  Given  the  Difference  of  Latitude  and  Distance 

run,  to  find  the  Difference  of  Longitude,  and 
Angle  of  the  Course  -  -  -  -  134 

46.  Given  the  difference  of  Longitude  and  Course,  to 

find  the  difference  of  Latitude,  and  Distance 


sailed  -  -  -  -  *  '  -  lo5 

47.  Given  the  Course  and  Distance,  to  find  the 

Difference  of  Longitude  and  Latitude  -  136 

48.  To  steer  a  ship  upon  the  Arch  of  a  great  Circle, 

£cc.  -------  137 

Of  the  Celestial  Globe  -  -  -  -  -  151 

Of  the  Pi'ccession  of  the  Equinoxes  -  -  -  157 


VI 


CONTENTS. 


Problem.  •  Pag6’ 

2.  To  rectify  the  Celestial  Globe  -  -  163 

3.  To  find  the  Declination  and  Right  Ascension  of  the 

Sun  -  -  -  -  -  -  -164 

4.  To  find  the  Sun’s  oblique  Ascension,  Sec.  -  165 

5.  - the  Sun’s  meridian  Altitude  -  166 

6.  - the  Length  of  the  Day  in  Latitudes  under 

66-1  Degrees  -  -  -  166 

7.  - the  Length  of  the  longest  and  shortest  Day 

m  Latitudes  under  6 6|  Degrees  -  7  -  167 

8.  To  find  the  Latitude  where  the  longest  Day  may 

be  of  any  given  Length  between  twelve  and 
twenty  four  Hours  -  -  -  167 

9. - the  time  of  Sun-rising,  Sec.  -  -  168 

10.  - how  long,  Sec.  the  Sun  shines  in  any  Place 

within  the  Polar  Circles  -  -  170 

1 1.  To  illustrate  the  Equation  of  Time,  See.  -  174 

12.  To  find  the  Right  Ascension,  8ec.  of  a  Star  -  176 

13.  - i —  the  Latitude  and  Longitude  of  a  Star  -  177 

14.  - the  Place  of  a  Star  on  the  Globe  by,  See.  177 

15.  - at  what  hour  a  given  Star  transits  the 

meridian  -  -  -  -  -  178 

16.  On  what  Day  a  Star  will  come  to  the  Meridian  179 

17.  To  represent  the  Face  of  the  Heavens  for  any 

given  Day  and  Hour  -  -  -  179 

18.  To  trace  the  Circles  of  the  sphere  in  the  Heavens  182 

19.  To  find  the  Circle  of  perpetual  Apparition  188 

20.  - the  Sun’s  Amplitude  -  -  -  189 

21.  - -the  Sun’s  Altitude  at  a  given  Hour  -  190 

22.  - - —  when  the  Sun  is  due  East  in  a  given  Lati¬ 

tude  -  -  -  -  -  193 


- the  Rising,  Setting,  Culminating,  Sec.  of  a 

Star  -  -  -  -  -  194 


- the  Hour  of  the  Day,  the  Altitude  and 

Azimuth  of  a  Star  being  given  -  -  195 

- the  Altitude  and  Azimuth  of  a  Star,  See.  196 


CONTENTS.  '  vii 

Problem.  rage. 

26.  - - —  the  Azimuth,  Sec.  at  any  Hour  of  the 

Night  -  -  -  -  -  197 

27.  - - -  the  Sun’s  Altitude,  and  the  Hour,  from 

the  Latitude,  Sun’s  Place,  and  Azimuth  197 

2 1 .  — - the  Hour,  the  Latitude  and  Azimuth 

given  -  -  -  -  -  198 

29.  - - a  Star,  the  Latitude,  Sun’s  Place,  Hour, 

Sec.  given  -  -  -  -  -  199 

30.  To  find  the  Hour  by  Data  from  two  Stars  that 

have  the  same  Azimuth  -  -  -  199 

31.  — - —  the  Hour  by  Data  from  two  Stars  that 

have  the  same  Altitude  -  200 

32.  — — —  the  Latitude  by  Data  from  two  Stars  201 

33.  - — —  the  Latitude  by  other  Data  from  two  Stars  201 

34.  — — — -  when  a  Star  rises  or  set  cosmically  -  203 

35.  - - -  when  a  Star  rises  or  sets  achronically  -  204 

36.  — — —  when  a  Star  will  rise  heliacaily  -  206 

37.  - when  a  Star  will  set  heliacaily  -  -  207 

Of  the  Correspondence  between  the  Celestial  and  Ter¬ 
restrial  Spheres  -----  208 

28.  To  find  the  Place  of  a  Planet,  See.  -  -  212 

39.  — - what  Planets  are  above  the  Horizon  -  213 

40.  - - the  right  Ascension,  & c.  of  a  Planet  -  214 

41.  — - the  Moon’s  Place  -  220 

42.  - - - the  Moon’s  Declination  -  -  -  221 

43.  - The  Moon’s  greatest  and  least  Meridian 

Altitudes  -  -  -  -  -  -  222 

44.  To  illustrate  the  Harvest  Moon  -  -  -  223 

45.  To  find  the  Azimuth  of  the  Moon,  and  thence 

High  Water,  Sec.  -  -  -  -  -  228 

Of  Comets  -  229 

46.  To  rectify  the  Globe  for  the  Place  of  Observation  231 

47.  To  determine  the  Place  of  a  Comet  -  -  232 

48.  To  find  the  Latitude,  Sec.  of  a  Comet  -  -  232 

49.  To  find  the  Time  of  a  Comet’s  Rising,  Sec,  -  233 


via 


CONTENTS. 


Problem.  Pag?. 

50.  To  find  the  same  at  London  ....  234 

5 1.  To  determine  the  Place  of  a  Comet  from  an  Obser¬ 

vation  made  at  London  -  -  234 

52.  From  two  given  Places  to  assign  the  Comet’s 

Path . 235 

53.  To  estimate  the  Velocity  of  a  Comet  -  -  236 

54.  To  represent  the  general  Phenomena  of  a  Comet  237 


1 


PREFACE 


TO  THE  ESSAY  ON  THE  GLOBES. 

/ 

>  V* 

rp 

1  HE  connection  of  astronomy  with  geography 
is  so  evident,  and  both  in  conjunction  so  nece  s¬ 
sary  to  a  liberal  education,  that  no  man  will  be 
thought  to  have  deserved  ill  of  the  republic  of 
letters,  who  has  applied  his  endeavours  to  dif¬ 
fuse  more  universally  the  knowledge  of  these 
useful  Sciences,  or  to  render  the  attainment 
of  them  easier  ;  for  as  no  branch  of  literature 
can  be  fully  comprehended  without  them,  so 
there  is  none  which  impresses  more  pleasing 
ideas  on  the  mind,  or  that  affords  it  a  more  ra¬ 
tional  entertainment. 

In  the  present  work,  several  objections  to 
former  editions  are  obviated  ;  the  Problems  ar- 
ranged  in  a  more  methodical  manner,  and  a 
great  number  added.  Such  facts  are  also  oc- 


u 


PREFACE. 


casionally  introduced,  such  observations  inter¬ 
spersed,  and  such  relative  information  commu¬ 
nicated,  as  it  is  presumed  will  excite  curiosity, 
and  fit  attention. 

To  further  the  design,  the  attention  is  direct¬ 
ed  to  the  appearance  of  the  planetary  bodies, 
as  observed  from  the  earth.  It  were  to  be 
wished  that  the  tutor  would  at  this  part  exhi¬ 
bit  to  his  pupil  the  various  phenomena  in  the 
heavens  themselves  ;  by  teaching  him  thus  to 
observe  for  himself,  he  would  not  only  raise  his 
curiosity,  but  so  fix  the  impressions  which  the 
objects  have  made  on  his  mind,  that  by  proper 
cultivation  they  would  prove  a  fruitful  source 
of  useful  employment ;  and  he  would  therby 
also  gratify  that  eager  desire  after  novelty, 
which  continually  animates  young  minds,  and 
furnishes  them  with  objects  on  which  to  exer¬ 
cise  their  natural  activity. 


PART  I. 


A  TREATISE 

ON  THE  USE  OF  THE  TERRESTRIAL  AND 
■CELESTIAL  GLOBES. 


OF  THE  ADVANTAGES  OF  GLOBES  IN  GENERAL,  FOR  IL¬ 
LUSTRATING  THE  PRIMARY  PRINCIPLES  OF  ASTRONO¬ 
MY  AND  GEOGRAPHY;  AND  PARTICULARLY  OF  THE 
ADVANTAGES  OF  THE  GLOBES,  WHEN  MOUNTED  IN  MY 
FATHER’S  MANNER. 

UNIVERSAL  approbation,  the  opinion  of 
those  that  excel  in  science,  and  the  ex* 
perience  of  those  that  are  learning,  all  concur 
to  prove  that  the  artificial  representations  of  the 
earth  and  heavens,  on  the  terrestrial  and  celestial 
globes,  are  the  instruments  the  best  adapted  to 
convey  natural  and  genuine  ideas  of  astronomy 
and  geography  to  young  minds. 

This  superiority  they  derive  principally 
from  their  form  and  figure,  which  communi¬ 
cates  a  more  just  idea,  and  gives  a  more  ade~ 

B  195 


10 


DESCRIPTION  AND  USE 


quate  representation  of  the  earth  and  heavens, 
than  can  be  formed  from  any  other  figure. 

To  understand  the  nature  of  the  projection 
of  either  sphere  in  piano,  requires  more  know¬ 
ledge  of  geometry  than  is  generally  possessed 
by  beginners,  it’s  principles  are  more  recluse, 
and  the  solution  of  problems  more  obscure. 

The  motion  of  the  earth  upon  it’s  axis  is 
one  of  the  most  important  principles  both  in 
geography  and  astronomy ;  on  it  the  greater 
part  of  the  phenomena  of  the  visible  world  de¬ 
pend :  but  there  is  no  invention  that  can  com¬ 
municate  so  natural  a  representation  of  this 
motion,  as  that  of  a  terrestrial  globe  about  it’s 
axis.  By  a  celestial  globe,  the  apparent  mo¬ 
tion  of  the  heavens  is  also  represented  in  a  na¬ 
tural  and  satisfactory  manner. 

In  order  to  convey  a  clear  idea  of  the  va¬ 
rious  divisions  of  the  earth,  of  the  situation  of 
different  places,  and  to  obtain  an  easy  solution 
of  the  various  problems  in  geography,  it  is 
necessary  to  conceive  many  imaginary  circles 
delineated  on  it’s  surface,  and  to  understand 
their  relation  to  each  other.  Now  on  a  globe 
these  circles  have  their  true  form  ;  their  inter¬ 
sections  and  relative  positions  are  visible  upon 
the  most  cursory  inspection.  But  in  projec¬ 
tions  of  the  sphere  in  piano,  the  form  of  these 
circles  is  varied,  and  their  nature  changed ; 
they  are  consequently  but  ill  adapted  to  convey 

196 


OF  THE  GLOBES. 


II 


to  young  minds  the  elementary  principles  of 
geography. 

On  a  globe,  the  appearance  of  the  land 
and  water  is  perfectly  natural  and  continuous, 
fitted  to  convey  accurate  ideas,  and  leave  per¬ 
manent  impressions  on  the  most  tender  minds  ; 
whereas  in  planispheres  one-half  of  the  globe 
is  separated  and  disjoined  from  the  other  ;  and 
those  parts,  which  are  contiguous  on  a  globe, 
are  here  separated  and  thrown  at  a  distance 
from  each  other.  The  celestial  globe  has  the 
same  superiority  over  projections  of  the  heavens 
in  piano. 

The  globe  exhibits  every  thing  in  true  propor¬ 
tion,  both  of  figure  and  size ;  while  on  a  planis¬ 
phere  the  reverse  may  often  be  observed. 

Presuming  that  these  reasons  sufficiently 
evince  the  great  advantage  of  globes  over 
either  planispheres  or  maps,  for  obtaining  the 
first  principles  of  astronomical  and  geographi¬ 
cal  knowledge,  I  proceed  to  point  out  the  pre¬ 
eminence  of  globes  mounted  in  my  father's  man - 
ner^  over  the  common,  or  rather  the  old  and 
Ptolemaic  mode  of  fitting  them  up. 

The  great  and  increasing  sale  of  his  globes 
mounted  in  the  best  manner,  may  be  looked 
upon  at  least  as  a  proof  of  approbation  from 
numbers ;  to  this  I  might  also  add,  the  en¬ 
couragement  they  have  received  fiom  the 
principal  tutors  of  both  our  universities,  the. 

197 


12 


description  and  use 


public  sanction  of  the  university  of  Leyden,* 
the  many  editions  of  my  father’s  treatise  on 
their  use,  and  its  translation  into  Dutch,  &c.. 
The  recommendation  of  Mess.  Arden,  Walker, 
Burton,  &c.  public  lecturers  in  natural  philoso¬ 
phy,  might  also  be  adduced :  but  leaving  these 
considerations,  I  shall  proceed  to  enumerate 
the  reasons  which  give  them,  in  my  opinion, 
a  decided  preference  over  every  other  kind  of 
mounting.* 

*  The  following  note  from  Mr.  Walker’s  Easy  Intro¬ 
duction  to  Geography,  in  favour  of  my  father’s  globes, 
will  not,  I  hope,  be  deemed  improper. 

“  Simplicity  and  perspicuity  should  ever  be  studied  by 
those  who  cultivate  the  young  mind ;  and  jarring,  oppos¬ 
ing,  or  equivocal  ideas  should  be  avoided  almost  as  much 
as  error  or  falsehood.  Our  globes,  till  of  late  years, 
were  equipt  with  an  hour  circle,  which  prevented  the 
poles  from  sliding  through  the  horizon  ;  hence  their  rec¬ 
tification  was  generally  for  the  place  on  the  earth ,  instead 
of  the  sun's  place  in  the  ecliptic  ;  which  put  the  globe  into 
so  unnatural  and  absurd  a  position  respecting  the  sun, 
that  young  people  were  confounded  when  they  compared 
it  with  the  earth’s  positions  during  it’s  annual  rotation 
round  that  luminary,  and  considering  the  horizon  as  the 
boundary  of  day  and  night.  Being,  therefore,  sometimes 
obliged  to  rectify  for  the  place  on  the  earth,  and  some¬ 
times  for  the  sun’s  place  in  the  ecliptic,  the  two  rules 
clash  so  unhappily  in  the  pupil’s  mind,  that  few  re¬ 
member  a  single  problem  a  twelvemonth  after  the  end 
of  their  tuition.  Globes,  therefore,  with  a  horary  cir¬ 
cle,  are  but  partially  described  in  this  treatise  ;  the 
great  intention  of  which  is,  to  make  the  elevations  and 

*  X9& 


OF  THE  GLOBES. 


43 


The  earth,  by  it’s  diurnal  revolution  on  it’s 
axis,  is  carried  round  from  west  to  east.  To 
represent  this  real  motion  of  the  earth,  and  to 
solve  problems  agreeable  thereto,  it  is  necessary 
that  the  globe,  in  the  solution  of  every  problem, 
should  be  moved  from  west  to  east ;  and  for  this 
purpose,  that  the  divisions  on  the  large  brass  cir¬ 
cle  should  be  on  that  side  which  looks  westward.* 
Now  this  is  the  case  in  my  father’s  mode  of 
mounting  the  globes,  and  the  tutor  can  thereby 
explam  with  ease  the  rationale  of  any  problem  to 
his  pupil.  But  in  the  common  mode  of  mount¬ 
ing,  the  globe  must  be  moved  from  east  to  west, 
according  to  the  Ptolemaic  system  ;  and  conse¬ 
quently,  if  the  tutor  endeavours  to  shew  how 
things  obtain  in  nature,  he  must  make  his  pupil 
unlearn  in  a  degree  what  he  has  taught  him,  and 
by  abstraction  reverse  the  method  he  has  instruct¬ 
ed  him  to  use  ;  a  practice  that  we  hope  will  not 
be  adopted  by  many. 

depressions  of  the  poles  of  a  terrestrial  globe  to  repre¬ 
sent  all  the  situations  the  earth  is  in  to  the  sun,  for  every¬ 
day  or  hour  through  the  year.  The  globes  of  Mr.  Adams. 
are  the  most  favourable  for  the  above  mode  of  rectification 
of  any  plates  we  have  at  present ;  and  to  make  a  quiescent 
glube  to  represent  all  the  positions  of  one  revolving  round 
the  sun,  turning  on  an  inclined  axis,  and  keeping  that  axis- 
altogether  parallel  to  itself,  his  globes  are  better  adapted 
than  any,  I  believe,  in  being.” 

*  See  the  Rev.  Mr.  Hutcnin’s  New  T realise  on  the  Globes- 

199 


14 


DESCRIPTION  AND  USE 


The  celestial  globe  being  intended  to  re¬ 
present  the  apparent  motion  of  the  heavens, 
should  be  moved,  when  used,  from  east  to 
west. 

< t  v 

Of  the  phenomena  to  be  explained  by  the 
terrestrial  globe,  the  most  material  are  those 
which  relate  to  the  changes  in  the  seasons ;  all 
the  problems  connected  with,  or  depending 
upon  these  phenomena,  are  explained  in  a 
clear,  familiar,  and  natural  manner,  by  the 
globe,  when  mounted  in  my  father’s  mode ;  for 
on  rectifying  it  for  any  particular  day  of  the 
month,  it  immediately  exhibits  to  the  pupil 
the  exact  situation  of  the  globe  of  the  earth  for 
that  day  ;  and  while  he  is  solving  his  problem, 
the  reason  and  foundation  of  it  presents  itself 
to  the  eye  and  understanding. 

The  globe  may  also  be  placed  with  ease  in 
the  position  of  a  right  sphere  ;  a  circumstance 
exceedingly  useful,  and  which  the  old  con¬ 
struction  of  the  globes  did  not  admit  of. 

By  the  application  of  a  moveable  meridian, 
and  an  artificial  horizon  connected  with  it,  it 
is  easy  to  explain  why  the  sun,  although  he  be 
'always  in  one  and  the  same  place,  appears  to 
the  inhabitants  of  the  earth  at  different  alti¬ 
tudes,  and  in  different  azimuths,  which  cannot 
he  so  readily  done  with  the  common  globes. 

On  the  celestial  globe  there  is  a  moveable 
circle  of  declination,  with  an  artificial  sun. 

200 


or  THE  GLOBES. 


15 


The  brass  wires  placed  under  the  globes, 
serve  to  distinguish,  in  a  natural  and  satisfacto¬ 
ry'  manner,  twilight  from  total  darkness,  and  the 
reason  of  the  length  of  it’s  duration. 

The  next  point,  wherein  they  materially  dif¬ 
fer  from  other  globes,  is  in  the  hour  circle. 
Now  it  must  be  confessed,  that  to  every  contri¬ 
vance  that  has  been  used  for  this  purpose  there 
is  some  objection,  and  probably  no  mode  can 
be  hit  upon  that  will  be  perfectly  free  from 
them.  The  method  adopted  by  my  father  ap¬ 
pears  to  me  the  least  exceptionable,  and  to 
possess  some  advantages  over  every  other  me¬ 
thod  I  am  acquainted  with.  Agreeably  to  the 
opinion  of  the  first  astronomers,  among  others 
of  M,  de  la  Lande,  he  uses  the  equator  for  the 
hour  circle,  not  only  as  the  largest,  but  also  as 
the  most  natural  ciicle  that  could  be  employed 
for  that  purpose,  and  by  which  alone  the  solu¬ 
tion  of  problems  could  be  obtained  with  the 
greatest  accuracy.  As  on  the  terrestrial  globe, 
the  longitude  of  different  places  is  reckoned 
on  this  circle  ;  and  on  the  celestial,  the  right 
ascension  of  the  stars,  &c.  it  familiarizes  the 
young  pupil  with  them,  and  their  reduction  to 
time.  This  method  does  not  in  the  least  im¬ 
pede  the  motion  of  the  globe  ;  but  wdiile  it 
affords  an  equal  facility  of  elevating  either  the 
north  or  south  pole,  it  prevents  the  pupil  from 

placing  them  in  a  wrong  position ;  while  the 

201 


16 


DESCRIPTION  AND  USE 


horary  wire  secures  the  globe  from  falling  out 
of  the  frame. 

Another  circumstance  peculiar  to  these  globes, 
is  the  mode  of  fixing  the  compass.  It  is  self- 
evident,  that  the  tutor,  who  is  willing  to  give 
correct  ideas  to  his  pupil,  should  always  make 
him  keep  the  globes  with  the  north  pole  direct¬ 
ed  towards  the  north  pole  of  the  heavens,  and 
that,  both  in  the  solution  of  problems,  and  the 
explanation  of  phenomena.  By  means  of  the 
compass,  the  terrestrial  globe  is  made  to  supply 
the  purpose  of  a  tellurian,  when  such  an  instru¬ 
ment  is  not  at  hand.  I  cannot  terminate  this  pa¬ 
ragraph,  without  testifying  my  disapprobation 
of  a  mode  adopted  by  some,  of  making  the  globe 
turn  round  upon  a  pin  in  the  pillar  on  which  it 
is  supported;  a  mode,  that,  while  it  can  give 
little  but  relief  to  indolence,  is  less  firm  in  it’s 
construction,  and  tends  to  introduce  much  con¬ 
fusion  in  the  mind  of  the  pupil. 

In  order  to  prevent  that  confusion  and  per¬ 
plexity  which  necessarily  arises  in  a  young 
mind,  when  names  are  made  use  of  which  do 
not  properly  characterize  the  subject,  my  fa¬ 
ther  found  it  necessary,  with  Mr.  Hutchins, 
to  term  that  broad  wooden  circle  which  sup¬ 
ports  the  globe,  and  on  which  the  signs  of  the 
ecliptic  and  the  days  of  the  month  are  engraved, 
the  broad  paper  circle ,  instead  of  horizon,  by 

202 


OF  THE  GLOBES. 


17 


which  it  had  been  heretofore  denominated. 
The  propriety  of  this  change  will  be  evident  to 
all  those  who  consider,  that  this  circle  in  some 
cases  represents  that  which  divides  light  from 
darkness,  in  others  the  horizon,  and  some¬ 
times  the  ecliptic.  For  similar  reasons,  he  was 
induced  to  call  the  brazen  circle,  in  which  the 
globes  are  suspended,  the  strong  brass  circle . 

In  a  word,  many  operations  may  be  perform¬ 
ed  by  these  globes,  which  cannot  be  solved  by 
those  mounted  in  the  common  manner ;  while 
a1'  that  they  can  solve  may  be  performed  by 
these,  and  that  with  a  greater  degree  of  perspi¬ 
cuity  ;  and  many. problems  may  be  performed 
by  these  at  one  view,  which  on  the  other  globes 
require  successive  operations. 

But  as,  notwithstanding  their  superiority, 
the  difference  in  price  may  make  some  persons 
prefer  the  old  construction,  it  may  be  proper 
to  inform  them,  that  they  may  have  my  father’s 
globes  mounted  in  the  old  manner ,  at  the  usual 
prices. 


nunoif^ui 


C  203 


' .? 


PAR T  II. 

4 


CONTAINING 

t 

A  DESCRIPTION  OF  THE  GLOBES  MOUNTED  IN 
THE  BEST  MANNER;  TOGETHER  WITH  SOME 
PRELIMINARY  DEFINITIONS. 


DEFINITIONS. 

BiEFORE  we  begin  to  discribe  the  globes, 
it  will  be  proper  to  take  some  notice  of 
the  properties  of  a  circle,  of  which  a  globe  may 
be  said  to  be  constituted. 

A  line  is  generated  by  the  motion  of  a  point. 
Let  there  be  supposed  two  points,  the  one 
moveable,  the  other  fixed. 

If  the  moveable  point  be  made  to  move  direct¬ 
ly  towards  the  fixed  point,  it  will  generate  in 
it’s  motion  a  straight  line. 

If  a  moveable  pomt  be  carried  round  a  fixed 
point,  keeping  always  the  same  distance  from 
it,  it  will  generate  a  circle,  or  some  part 

204 


OF  THE  GLOBES, 


19 


of  a  circle,  and  the  fixed  point  will  be  the 
center  of  that  circle. 

All  strait  lines  going  from  the  center  to  the 
•  circumference  of  a  circle,  are  equal. 

Every  strait  line  that  passes  through  the  cen¬ 
ter  of  a  globe,  and  is  terminated  at  both  ends 
by  it’s  surface,  is  called  a  diameter . 

The  extremities  of  a  diameter  are  it’s  poles. 

If  the  circumference  of  a  semicircle  be  turned 
round  it?s  diameter,  as  on  an  axis,  it  will  gene¬ 
rate  a  globe,  or  sphere. 

The  center  of  the  semicircle  will  be  the  cen¬ 
ter  of  the  globe ;  and  as  all  points  of  the  gene¬ 
rating  semicircle  are  at  an  equal  distance  from 
it’s  center,  so  all  the  points  of  the  surface  of 
the  generated  sphere  are  at  an  equal  distance 
from  it’s  center. 

DESCRIPTION  OF  THE  GLOBES, 

There  are  two  artificial  globes.  On  the  sur¬ 
face  of  one  of  them  the  heavens  are  delineated  ; 
this  is  called  the  celestial  globe .  The  other,  on 
which  the  surface  of  the  earth  is  described,  is 
called  the  terrestrial  globe . 

Fig.  2,  plate  XIII,  represents  the  celestial, 
fig.  l ,  plate  XIII,  the  terrestrial  globe,  as  mount¬ 
ed  in  my  father’s  manner. 

205 


description  and  use 


20 

In  using  the  celestial  globe,  we  are  to  consider 
ourselves  as  at  the  center . 

In  using  the  terrestrial  globe,  we  are  to 
suppose  ourselves  on  some  point  of  it’s  sur¬ 
face . 

The  motion  of  the  terrestrial  globe  repre¬ 
sents  the  real  motion  of  the  earth. 

The  motion  of  the  celestial  globe  represents 
the  apparent  motion  of  the  heavens. 

The  motion,  therefore,  of  the  celestial  globe, 
is  a  motion  from  east  to  west . 

But  the  motion  of  the  terrestrial  globe  is  a 
motion  from  west  to  east . 

On  the  surface  of  each  globe  several  circles 
are  described,  to  every  one  of  which  may  be  ap¬ 
plied  what  has  been  said  of  circles  in  page  205. 

The  center  of  some  of  these  circles  is  the 
same  with  the  center  of  the  globe ;  these  are, 
by  way  of  distinction,  called  great  circles . 

Of  these  great  circles,  some  are  graduated. 

The  graduated  circles  are  divided  into  360, 
or  equal  parts,  90  of  which  make  a  quarter  of  a 
circle,  or  a  quadrant. 

Those  circles,  whose  centers  do  not  pass 
through  the  center  of  the  globe,  are  called  lesser 

circles . 

The  globes  are  each  of  them  suspended  at 
the  poles  in  a  strong  brass  circle  N  Z  JE  S,  and 
turn  therein  upon  two  iron  pins,  which  are 

206 


OF  THE  GLOBES. 


21 


(he  axis  of  the  globe  ;  they  have  each  a  thin  brass 
semicircle  N  H  S,  moveable  about  these  poles, 
with  a  small  thin  circle  H  sliding  thereon :  it 
is  quadrated  each  way  to  90°  from  the  equator 
to  either  pole. 

On  the  terrestrial  globe  this  semicircle  is  a 
moveable  meridian .  It’s  small  sliding  circle, 
which  is  divided  into  a  few  of  the  points  of  the 
mariner’s  compass,  is  called  a  terrestrial  or 
visible  horizon. 

On  the  celestial  globe  this  semicircle  is  a 
moveable  circle  of  declination ,  and  it’s  small  brass 
circle  an  artificial  sun,  or  planet. 

Each  globe  has  a  brass  wire  circle,  T  W  Y, 
placed  at  the  limits  of  the  crepusculum,  or  twi¬ 
light,  which,  together  with  the  globe,  is  mount¬ 
ed  in  a  wooden  frame.  The  upper  part,  B  C, 
is  covered  with  a  broad  paper  circle,  whose 
plane  divides  the  globe  into  twTo  hemispheres  ; 
and  the  whole  is  supported  by  a  neat  pillar  and 
claw,  with  a  magnetic  needle  in  a  compass-box, 
marked  M. 

.  t 

A  DESCRIPTION  OF  THE  CIRCLES  DESCRIBED 
ON  THE  BROAD  PAPER  CIRCLES  B  C  ;  TO¬ 
GETHER  WITH  A  GENERAL  ACCOUNT  OF 
it’s  USES. 

It  contains  four  concentric  circular  spaces, 
the  innermost  of  which  is  divided  into  360°, 

207 


22 


DESCRIPTION  AND  USE 


and  numbered  into  four  quadrants,  beginning  at 
the  east  and  west  points,  and  proceeding  each 
•way  to  90°,  at  the  north  and  south  points  : 
these  are  the  four  cardinal  points  of  the  hori¬ 
zon.  The  second  circular  space  contains,  at 
equal  distances,  the  thirty-two  points  of  the 
mariner’s  compass.  Another  circular  space  is 
divided  into  twelve  equal  parts,  representing 
the  twelve  signs  of  the  zodiac  ;  these  are  again 
subdivided  into  30  degrees  each,  between  which 
are  engraved  their  names  and  characters.  This 
space  is  connected  with  a  fourth,  which  con¬ 
tains  the  calendar  of  the  months  and  days ; 
each  day,  on  the  eighteen-inch  globes  being 
divided  into  four  parts,  expressing  the  four 
cardinal  points  of  the  day,  according  to  the 
Julian  reckoning ;  by  which  means  the  sun’s 
place  is  very  nearly  obtained  for  the  common 
years  after  bissextile,  and  the  intercalary  day 
is  inserted  without  confusion. 

In  all  positions  of  the  celestial  globe,  this 
broad  paper  circle  represents  the  plane  of  the 
horizon,  and  distinguishes  the  visible  from  the 
invisible  part  of  the  heavens ;  but  in  the  ter¬ 
restrial  globe ,  it  is  applied  to  three  different 
uses . 

1.  To  distinguish  the  points  of  the  horizon. 
In  this  case  it  represents  the  rational  horizon  of 
any  place. 

2.  It  is  used  to  represent  the  circle  of 

208 


OF  THE  GLOBES. 


23 

illumination ,  or  that  circle  which  separates  day 
from  night. 

3.  It  occasionally  represents  the  ecliptic . 

Of  the  strong  brass  circle  N  JE  Z  S.  One  side 
of  this  strong  brass  circle  is  graduated  into  four 
quadrants,  each  containing  90  degrees. 

The  numbers  on  two  of  these  quadrants  in¬ 
crease  from  the  equator  towards  the  poles ; 
the  other  two  increase  from  the  poles  towards 
the  equator. 

Two  of  the  quadrants  are  numbered  from 
the  equator,  to  shew  the  distance  of  any  point 
on  the  globe  from  the  equator.  The  other 
two  are  numbered  from  the  poles,  for  the  more 
ready  setting  the  globe  to  the  latitude  of  any 
place. 

The  strong  brass  circle  of  the  celestial  globe 
is  called  the  meridian,  because  the  centre  of  the 
sun  comes  directly  under  it  at  noon. 

But  as  there  are  other  circles  on  the  ter¬ 
restrial  globe,  which  are  called  meridians,  we 
chuse  to  denominate  this  the  strong  brass  circle , 
or  meridian . 

The  graduated  side  of  the  strong  brass  circle, 
that  belongs  to  the  terrestrial  globe,  should  face 
the  west . 

The  graduated  side  of  the  strong  brazen 
meridian  of  the  celestial  globe,  should  face  the 
east , 


209 


24 


DESCRIPTION  AND  USE 


On  the  strong  brass  circle  of  the  terrestrial 
globe,  and  at  about  23'  degrees  on  each  side 
of  the  north  pole,  the  days  of  each  month  are 
laid  down  according  to  the  declination  of  the 
sun. 

Of  the  Horary  Circles ,  and  their  Indices. 
When  the  globes  are  mounted  in  my  father’s 
manner,  we  use  the  equator  as  the  hour  circle ; 
because  it  is  not  only  the  most  natural,  but 
also  the  largest  circle  that  can  be  applied  for 
that  purpose. 

To  make  this  circle  answer  the  purpose,  a 
semi-circular  wire  is  placed  over  it,  carrying 
two  indices,  one  on  the  east,  the  other  on  the 
west  side  of  the  strong  brass  circle. 

As  the  equator  is  divided  into  360°,  or  24 
hours,  the  time  of  one  entire  revolution  of  the 
earth  or  heavens,  the  indices  will  shew  in  what 
space  of  time  any  part  of  such  revolution  is 
made  among  the  hours  which  are  graduated 
below  the  degrees  of  the  equator  on  either 
globe. 

As  the  motion  of  the  terrestrial  globe  is 
from  west  to  east,  the  horary  numbers  increase 
according  to  the  direction  of  that  motion :  on 
the  celestial  globe  they  increase  from  the  east  to 
the  west. 

Of  the  Quadrant  of  Altitude ,  Z  A.  This  is 
a  thin,  narrow,  flexible  slip  of  brass,  that  will 
bend  to  the  surface  of  the  globe  ;  it  has  a  nut, 

210 


OF  THE  GLOBES. 


25 


with  a  fiducial  line  upon  it,  which  may  be 
readily  applied  to  the  divisions  on  the  strong 
brass  meridian  of  either  globe.  One  edge  of 
the  quadrant  is  divided  into  90  degrees,  and 
the  divisions  are  continued  to  18  degrees  below 
the  horizon. 

v 

OF  SOME  OF  THE  CIRCLES  THAT  ARE  DESCRIB¬ 
ED  UPON  THE  SURFACE  OF  EACH  GLOBE. 

We  may  suppose  as  many  circles  to  be  de¬ 
scribed  on  the  surface  of  the  earth  as  we  please, 
and  conceive  them  to  be  extended  to  the 
sphere  of  the  heavens,  making  thereon  con¬ 
centric  circles  :  for  as  we  are  obliged,  in  order 
to  distinguish  one  place  from  another,  to  ap¬ 
propriate  names  to  them,  so  are  we  obliged  to 
use  different  circles  on  the  globes,  to  distinguish 
their  parts,  and  their  several  relations  to  each 
other. 

Of  the  Equator ,  or  Equinoctial,  This  circle 
goes  round  the  globe  exactly  in  the  middle,  be¬ 
tween  the  two  poles,  from  which  it  always 
keeps  at  the  same  distance ;  or  in  other  words, 
it  is  every  where  90  degrees  distant  from  each 
pole,  and  is  therefore  a  boundary,  separating 
the  northern  from  the  southern  hemisphere ; 
hence  it  is  frequently  called  the  line  by  sailors, 
and  when  they  sail  over  it  they  are  said  to  cross 
the  line. 


D  211 


26  DESCRIPTION  AND  USE 

\ 

It  is  that  circle  in  the  heavens  in  which 
the  sun  appears  to  move  on  those  two  days, 
the  one  in  the  spring,  the  other  in  the  autumn, 
when  the  days  and  nights  are  of  an  equal 
length  all  over  the  world  ;  and  hence  on  the 
celestial  globe  it  is  generally  called  the  equi¬ 
noctial . 

It  is  graduated  into  360  degrees.  Upon 
the  terrestrial  globe  the  numbers  increase  from 
the  meridian  of  London  westward,  and  pro¬ 
ceed  quite  round  to  360.  They  are  also  num¬ 
bered  from  the  same  meridian  eastward,  by  an 
upper  row  of  figures,  to  accomodate  those 
who  use  the  English  tables  of  latitude  and  lon¬ 
gitude. 

On  the  celestial  globe,  the  equatorial  degrees 
are  numbered  from  the  first  point  of  Aries  east¬ 
ward,  to  360  degrees. 

Under  the  degrees  on  either  globe  is  gra¬ 
duated  a  circle  of  hours  and  minutes.  On  the 
celestial  globe  the  hours  increase  eastward, 
from  Aries  to  XII  at  Libra,  where  they  begin 
again  in  the  same  direction,  and  proceed  to  XII 
at  Aries.  But  on  the  terrestrial  globe,  the 
horary  numbers  increase  by  twice  twelve  hours 
westward  from  the  meridian  of  London  to  the 
same  again. 

In  turning  the  globe  about,  the  equator 
keeps  always  under  one  point  of  the  strong 

212 


I 


OF  THE  GLOBES.  27 

brass  meridian,  from  which  point  the  degrees 
on  the  said  circle  are  numbered  both  ways. 

Of  the  Ecliptic .  The  graduated  circle,  which 
crosses  the  equator  obliquely,  forming  with 
it  an  angle  of  about  23 1  degrees,  is  called  the 
ecliptic. 

This  circle  is  divided  into  twelve  equal  parts, 
each  of  which  contains  thirty  degrees.  The 
beginning  of  each  of  these  thirty  degrees  is 
marked  with  the  characters  of  the  twelve  signs 
of  the  zodiac. 

The  sun  appears  always  in  this  circle  ;  he 
advances  therein  every  day  nearly  a  degree,  and 
goes  through  it  exactly  in  a  year. 

The  points  where  this  circle  crosses  the 
equator  are  called  the  equinoctial  points .  The 
one  is  at  the  beginning  of  Aries,  the  other  at 
the  beginning  of  Libra. 

The  commencement  of  Cancer  and  Capricorn 
are  called  the  solstitial  points . 

The  twelve  signs,  and  their  degrees,  are  laid 
down  on  the  terrestrial  globe  ;  but  upon  the 
celestial  globe,  the  days  of  each  month  are  gra¬ 
duated  just  under  the  ecliptic. 

The  ecliptic  belongs  principally  to  the  celes¬ 
tial  globe. 


PART  in. 


THE  USE  OF  THE  TERRESTRIAL  GLOBE? 
MOUNTED  IN  THE  BEST  MANNER. 


OF  LONGITUDE  AND  LATITUDE,  OF  TERRESTRIAL  MERI¬ 
DIANS,  AND  THE  PROBLEMS  RELATING  TO  LONGITUDE 
AND  LATITUDE. 

ERIDIANS  are  circular  lines,  going  over 


..v  !  the  earth’s  surface,  from  one  pole  to  the 
other,  and  crossing  the  equator  at  right  angles. 

Whatever  places  these  circular  lines  pass 
through,  in  going  from  pole  to  pole,  they  are 
the  meridians  of  those  places. 

There  are  no  places  upon  the  surface  of  the 
earth,  through  which  meridians  may  not  be  con¬ 
ceived  to  pass.  Every  place,  therefore,  is  sup¬ 
posed  to  have  a  meridian  line  passing  over  it’s 
zenith  from  north  to  south,  and  going  through 
the  poles  of  the  world. 

Thus  the  meridian  of  Paris  is  one  meri¬ 
dian  ;  the  meridian  of  London  is  another. 
This  variety  of  meridians  is  satisfactorily  re- 


214 


OF  THE  GLOBES. 


‘29 


presented  on  the  globe,  by  the  moveable  meri¬ 
dian,  which  may  be  set  to  every  individual  point 
of  the  equator,  and  put  directly  over  any  parti¬ 
cular  place. 

Whensoever  we  move  towards  the  east  or 
west,  we  change  our  meridian ;  but  we  do  not 
change  our  meridian  if  we  move  directly  to  the 
north  or  south. 

The  moveable  meridian  shews  that  the  poles 
of  the  earth  divide  every  meridian  into  two  semi¬ 
circles,  one  of  which  passes  through  the  place 
whose  meridian  it  is,  the  other  through  a  point 
on  the  earth,  opposite  to  that  place. 

Hence  it  is,  that  writers  in  geography  and 
astronomy  generally  mean  by  the  meridian  of 
any  place  the  semicircle  which  passes  through 
that  place  ;  these,  therefore,  may  be  called  the 
geographical  meridians. 

All  places  lying  under  the  same  semicircle, 
are  said  to  have  the  same  meridian  ;  and  the 
semicircle  opposite  to  it  is  called  the  opposite 
meridian,  or  sometimes  the  opposite  part  of  the 
meridian. 

From  the  foregoing  definitions,  it  is  clear  that 
the  meridian  of  any  place  is  immoveably  fixed 
to  that  place,  and  is  carried  round  along  with  it 
by  the  rotation  of  the  globe. 

When  the  meridian  of  any  place  is  by  the  re¬ 
volution  of  the  earth  brought  to  point  at  the  sun, 
it  is  noon,  or  mid-day,  at  that  place. 

215 


30 


DESCRIPTION  AND  USE 


The  plane  of  the  meridian  of  any  place  may 
be  imagined  to  be  extended  to  the  sphere  of 
the  fixed  stars. 

When,  by  the  motion  of  the  earth,  the  plane 
of  a  meridian  comes  to  any  point  in  the  heavens, 
as  the  sun,  moon,  &c.  that  point,  &c.  is  then 
said  to  come  to  the  meridian.  It  is  in  this  sense 
that  we  generally  use  the  expression  of  the  sun 
or  stars  coming  to,  or  passing  over  the  meridian. 

The  time  which  elapses  between  the  noon  of 
any  one  day  in  a  given  place,  and  the  noon  of 
the  day  following  in  the  same  place,  is  called  a 
natural  day. 

All  places  which  lie  under  the  same  meridian, 
have  their  noon,  and  every  other  hour  of  the 
natural  day,  at  the  same  time.  Thus  when  it  is 
one  in  the  afternoon  at  London,  it  is  also  one  in 
the  afternoon  to  every  place  under  the  meridian 
of  London. 

In  order  to  ascertain  the  situation  of  any 
point,  there  must  first  be  a  settled  part  of  the 
earth’s  surface,  from  which  to  measure ;  and  as 
the  point  to  be  ascertained  may  lie  in  any  part 
of  the  earth’s  surface,  and  as  this  surface  is 
spherical,  the  place  from  whence  we  measure 
must  be  a  circle.  It  would  be  necessary,  how* 
ever  to  establish  two  such  circles  ;  one  to  know 
how  far  any  place  may  be  east  or  west  of  ano¬ 
ther,  the  second  to  know  it’s  distance  north  or 

216 


OF  THE  GLOBES. 


Cl  J 
i. 


south  of  the  given  point,  and  thus  determine  it’s 
precise  situation. 

Hence  it  has  been  customary  for  geographers 
to  fix  upon  the  meridian  of  some  remarkable 
place,  as  a  first  meridian ,  or  standard ;  and  to 
reckon  the  distance  of  any  place  to  the  east  or 
west,  or  it’s  longitude,  by  it’s  distance  from  the 
first  meridian.  On  English  globes,  this  first 
meridian  is  made  to  pass  through  London.  The 
position  of  this  first  meridian  is  arbitrary,  because 
on  a  globe,  properly  speaking,  there  is  neither 
beginning  nor  end.  The  first  person  (whose 
works  at  least  are  come  down  to  us)  who  com¬ 
puted  the  distance  of  places  by  longitudes  and 
latitudes  was  Ptolemy,  about  the  year  after 
Christ  140. 

The  longitude  of  any  place  is  it’s  distance  from 
the  first  meridian,  measured  by  degrees  on  the 
equator. 

To  find  the  longitude  of  a  place,  is  to  find 
what  degree  on  the  equator  the  meridian  of  tliat 
place  crosses. 

All  places  that  lie  under  the  same  meridian, 
are  said  to  have  the  same  longitude;  all  places 
that  lie  under  different  meridians,  are  said  to 
have  different  longitudes  ;  this  difference  may 
be  east  or  west,  and  consequently  the  difference 
of  longitude  between  any  two  places,  is  the  dis¬ 
tance  of  their  meridians  from  each  other  measur¬ 
ed  on  the  eauator. 


21 7 


DESCRIPTION  AND  USE 


Thus  if  the  meridian  of  any  place  cuts  the 
equator  in  a  point,  which  is  fifteen  degrees 
east  from  that  point,  where  the  meridian  of 
London  cuts  the  equator,  that  place  is  said  to 
differ  from  London  in  longitude  15  degrees 
eastward. 

Upon  the  terrestrial  globe  there  are  24  meri¬ 
dians,  dividing  the  equator  into  24  equal  parts, 
which  are  the  hour  circles  of  the  places  through 
which  they  pass. 

The  distance  of  these  meridians  from  each 
other  is  15  degrees,  or  the  24th  part  of  360 
degrees  ;  thus  15  degrees  is  equal  to  one  hour. 

By  the  rotation  of  the  earth,  the  plane  of 
every  meridian  points  at  the  sun,  one  hour  af¬ 
ter  that  meridian  which  is  next  to  it  eastward  ; 
and  thus  they  successively  point  at  the  sun  every 
hour,  so  that  the  planes  of  the  24  meridian  semi¬ 
circles  being  extended,  pass  through  the  sun  in 
a  natural  day. 

To  illustrate  this,  suppose  the  plane  of  the 
strong  brass  meridian  to  coincide  with  the  sun, 
bring  London  to  this  meridian,  and  then  move 
the  globe  round,  and  you  will  find  these  24 
meridians  successively  pass  under  the  strong 
brass  meridian,  at  one  hour’s  distance  from 
each  other ;  till  in  24  hours  the  earth  wall  re¬ 
turn  to  the  same  situation,  and  the  meridian  of 

218 


OF  THE  GLOBES. 


33 


London  will  again  coincide  with  the  strong  brass 
circle. 

By  passing  the  globe  round,  as  in  the  fore¬ 
going  article,  it  will  be  evident  to  the  pupil, 
that  if  one  of  these  meridians,  15  degrees  east 
of  London,  comes  to  the  strong  brass  meridian, 
or  points  at  the  sun  one  hour  sooner  than  the 
meridian  of  London,  a  meridian  that  is  30  de¬ 
grees  east  comes  two  hours  sooner,  and  so  on ; 
and  consequently  they  will  have  noon,  and 
every  other  hour,  so  much  sooner  than  at  Lon¬ 
don  :  while  those,  whose  meridian  is  15  degrees 
westward  from  London,  will  have  noon  and 
every  other  hour  of  the  day,  one  hour  later  than 
at  London,  and  so  on,  in  proportion  to  the 
difference  of  longitude.  These  definitions  being 
well  understood,  the  pupil  will  be  prepared  not 
only  to  solve,  but  see  the  rationale  of  the  follow¬ 
ing  problems. 


PROBLEM  i. 

To  find  the  Longitude  of  any  place  on  the  Globe . 

The  reader  will  find  no  difficulty  in  solving 
this  problem,  if  he  recollects  the  definition  we 
have  given  of  the  word  longitude,  namely,  that 
it  is  the  distance  of  any  place  from  the  first 
meridian  measured  on  the  equator.  Ihere- 
fore,  either  set  the  moveable  meridian  to  the 
place,  or  bring  the  place  under  the  strong  brass 

E  219 


34 


description  and  use 


meridian,  and  that  degree  of  the  equator,  which 
is  cut  by  either  of  the  brazen  meridians,  is  the 
longitude  in  degrees  and  minutes,  or  the  hour 
and  minute  of  its  longitude,  expressed  in  time. 

As  the  given  place  may  lie  either  east  or  west 
of  the  first  meridian,  the  longitude  may  be  ex¬ 
pressed  accordingly. 

It  appears  most  natural  to  reckon  the  lon- 
.  gitude  always  westward  from  the  first  meridian ; 
but  it  is  customary  to  reckon  one  half  round 
the  globe  eastward,  the  other  half  westward 
from  the  first  meridian.  To  accomodate  those 
who  may  prefer  either  of  these  plans,  there  are 
two  sets  of  numbers  on  our  globes :  the  num¬ 
bers  nearest  the  equator  increase  westward,  from 
the  meridian  of  London  quite  round  the  globe 
to  360°,  over  which  another  set  of  numbers  is 
engraved,  which  increase  the  contrary  way ;  so 
that  the  longitude  may  be  reckoned  upon  the 
equator,  either  east  or  west. 

Example .  Bring  Boston,  in  New  England, 
to  the'  graduated  edge  of  either  the  strong  brass, 
or  of  the  moveable  meridian,  and  you  will  find 
it’s  longitude  in  degrees  to  be  70*,  or  4  h. 
42  min.  in  time ;  Rome  122  degrees  east,  or  50 
min.  in  time ;  Charles-Town,  North- America, 
is  79  deg.  50  min.  west. 

220 


OF  THE  GLOBES. 


PROBLEM  II. 

To  find  the  difference  of  longitude  between  any  two 

places. 

If  the  pupil  understands  what  is  meant  by  the 
difference  of  longitude,  the  rule  for  the  solution 
of  this  problem  will  naturally  occur  to  his  mind. 
Now  the  difference  of  longitude  between  any 
two  places  is  the  quantity  of  an  angle  (at  the 
pole)  made  by  the  meridians  of  those  places 
measured  on  the  equator.  To  express  this  angle 
upon  the  globe,  bring  the  moveable  meridian 
to  one  of  the  places,  and  the  other  place  under 
the  strong  brass  circle,  and  the  required  angle 
is  contained  between  these  two  meridians,  the 
measure  or  quantity  of  which  is  to  be  counted 
on  the  equator. 

Example .  I  find  the  longitude  of  Rome  to 
be  12*  east,  that  of  Constantinople  to  be  29  ; 
the  difference  is  17 J  degrees.  Again,  I  find 
Jerusalem  has  35  deg.  25  min.  east  longitude 
from  London;  and  Pekin,  in  China,  116  deg. 
52  min.  east  longitude ;  the  difference  is  81  deg. 
27  min. ;  that  is,  Pekin  is  81  deg.  27  min.  east 
longitude  from  Jerusalem;  or  Jerusalem  is  81 
deg.  27  min.  west  longitude  from  Pekin. 

If  one  place  is  east,  and  the  other  west  of 
the  first  meridian,  either  find  the  longitude  of 
both  places  westward,  by  that  set  of  numbers 

221 


36  description  and  use 

.  • 

which  increase  westward  from  the  meridian  of 
London  to  360  deg.  and  the  difference  between 
the  number  thus  found  is  the  answer  to  the 
question  : — or,  add  the  east  and  west  longitudes, 
and  the  sum  is  the  difference  of  longitude  \  thus 

the  longitude  of  Rome  is  12  deg.  30  min.  east, 

% 

of  Charles-Town  79  deg.  50  min,  west ;  their 
sum,  91  deg.  20  min.  is  the  difference  re- 
quired. 

It  may  be  proper  to  observe  here,  that  the 
difference  of  time  is  the  same  with  the  difference 
cf  longitude ,  consequently  that  some  of  the  fol¬ 
lowing  problems  are  only  particular  cases  of  this 
problem,  or  readier  modes  of  computing  this 
difference.  . 

PROBLEM  III. 

To  find  all  those  places  where  it  is  noon ,  at  any 
given  hour  of  the  day ,  at  any  given  place . 

General  rule .  Bring  the  given  place  to  the 
brass  meridian ;  and  set  the  index  to  the  upper¬ 
most  XII ;  then  turn  the  globe,  till  the  index 
points  to  the  given  hour,  and  it  will  be  noon  to 
all  the  places  under  the  meridian. 

As  the  diurnal  motion  of  the  earth  is  from 
west  to  east ,  it  is  plain  that  all  places  which  are 
to  the  east  of  any  meridian,  must  necessarily 
pass  by  the  sun  before  a  meridian  which  is  to 
the  west  can  arrive  at  it. 

222 


OF  THE  GLOBES. 


37 


N.  B.  As  in  my  father’s  globes,  the  XII,  or 
first  meridian,  passes  through  London,  you  have 
only  to  bring  the  given  hour  to  the  east  of 
London,  if  in  the  morning,  to  the  brass  meri¬ 
dian,  and  all  those  places  which  are  under  it 
will  have  noon  at  the  given  hour ;  but  bring 
the  given  hour  westward  of  London,  if  it  be  in 
the  afternoon. 

When  it  is  4  h.  50  min.  in  the  afternoon  at 
Paris,  it  is  noon  at  New  Britain,  New  England, 
St.  Domingo,  Terra  Firma,  Peru,  Chili,  and 
Terra  del  Fuego. 

When  it  is  7  h.  50  min.  in  the  morning  at 
Ispahan,  it  is  noon  at  the  middle  of  Siberia, 
Chinese  Tartary,  Ghina,  Borneo. 

PROBLEM  IV. 

When  it  is  noon  at  any  place ,  to  find  what  hour  of 
the  day  it  is  at  any  other  place. 

Rule.  Bring  the  place  at  which  it  is  noon, 
to  the  strong  brass  meridian,  and  set  the  hour 
index  to  the  uppermost  XII,  and  then  turn  the 
globe  about  till  the  other  place  comes  under 
the  strong  brass  meridian,  and  the  hour  index 
will  shew  upon  the  equator  the  required  hour. 
If  to  the  eastward  of  the  place  where  it  is 
noon,  the  hour  found  will  be  in  the  afternoon ; 
If  to  the  westward,  it  will  be  in  the  forenoon. 

223 


38 


description  and  use 


Thus  when  it  is  noon  at  London,  it  is  50  min. 
past  XII,  at  Rome ;  32  min.  past  VII  in  the 
evening  at  Canton,  in  China ;  15  min.  past  VII 
in  the  morning  at  Quebec,  in  Canada. 


problem  v. 

The  hour  being  given  at  any  place ,  to  tell  what 

hoar  it  is  in  any  other  part  of  the  world . 

Rule .  Bring  the  place  where  the  time  is  re¬ 
quired  under  the  strong  brass  meridian,  set  the 
hour  index  to  the  given  time,  then  turn  the 
globe,  till  the  other  place  is  under  the  brass 
meridian,  and  the  horary  index  will  point  to 
the  hour  required. 

Thus  suppose  we  are  at  London  at  IX  o’clock 
in  the  morning,  what  is  the  time  at  Canton,  in 
China?  Answer,  31  min.  past  IV  in  the  after¬ 
noon.  When  it  is  IX  in  the  evening  at  London, 
it  is  about  15  min.  past  IV  in  the  afternoon  at 
Quebec  in  Canada. 

Thus  also  when  it  is  III  in  the  afternoon  at 
London,  it  is  18  min.  past  X  in  the  forenoon  at 
Boston.  When  it  is  VI  in  the  morning  at  the 
Cape  of  Good  Hope,  it  is  7  min.  after  mid¬ 
night  at  Quebec. 


224 


OF  THE  GLOBES. 


39 


/ 

OF  LATITUDE. 


I  have  already  observed,  that  the  equator 
divides  the  globe  into  two  hemispheres,  the  nor¬ 
thern  and  the  southern. 

The  latitude  of  a  place  is  it’s  distance  from 
the  equator  towards  the  north  or  south  pole, 
measured  by  degrees  upon  the  meridian  of  the 
place. 

All  places,  therefore,  that  lie  under  the  equa¬ 
tor,  are  said  to  have  no  latitude . 

All  other  places  upon  the  earth  are  said  to 
be  in  north  or  south  latitude,  as  they  are  situated 
on  the  north  or  south  side  of  the  equator ;  and 
the  latitude  of  any  place  will  be  greater  or  less, 
according  as  it  is  farther  from,  or  nearer  to  the 
equator. 

Lines,  which  keep  always  at  the  same  distance 
from  each  other,  are  called  parallels . 

If  a  circle,  or  circular  line,  be  conceived  keep¬ 
ing  at  the  same  distance  from  the  equator,  it  will 
be  a  parallel  to  the  equator. 

Circles  of  this  kind  are  commonly  drawn 
on  the  terrestrial  globe,  on  both  sides  of  the 
equator. 

A  circle  of  this  kind,  at  10  degrees  from  the 
equator,  is  called  a  parallel  of  10  degrees. 

When  any  such  parallel  passes  through  two 

225 


40 


DESCRIPTION  AND  USE 


places  on  the  globe’s  surface,  those  two  places 
have  the  same  latitude. 

Hence  parallels  to  the  equator  are  called  pa* 

rallels  of  latitude . 

There  are  four  principal  lesser  circles  parallel 
to  the  equator,  which  divide  the  globe  into  five 
unequal  parts,  called  zones. 

The  circle  on  the  north  side  of  the  equator  is 
called  the  tropic  of  Cancer ;  it  just  touches  the 
north  part  of  the  ecliptic,  and  shews  the  path 
the  sun  appears  to  describe,  the  longest  day  in 
summer. 

That  which  is  cn  the  south  side  of  the  equa¬ 
tor  is  called  the  tropic  of  Capricorn ;  it  just 
touches  the  south  part  of  the  ecliptic,  and  shews 
the  path  the  sun  appears  to  describe,  the  short¬ 
est  day  in  winter. 

The  space  between  these  two  tropics,  which 
contains  about  47  degrees,  was  called  by  the  an¬ 
cients  the  torrid  zone . 

The  two  polar  circles  are  placed  at  the  same 
distance  from  the  poles,  that  the  two  tropics  are 
from  the  equator. 

One  of  these  is  called  the  northern ,  the  other 
the  southern  polar  circle . 

These  include  23*  degrees  on  each  side  of 
their  respective  poles,  and  consequently  contain 
47  degrees,  equal  to  the  number  of  degrees  in¬ 
cluded  between  the  tropics. 

The  space  contained  within  the  northern 

226 


OF  THE  GLOBES. 


41 


polar  circle,  was  by  the  ancients  called  the  north 
frigid  zone  ;  and  that  within  the  southern  polar 
circle,  the  south  frigid  zone . 

The  spaces  between  either  polar  circle,  and  its 
nearest  tropic,  which  contain  about  43  degrees 
each,  were  called  by  the  ancients  the  two  temperate 
zones . 

PROBLEM  VI. 

To  find  the  latitude  of  any  place . 

If  the  pupil  comprehends  the  foregoing  defi¬ 
nition,  he  will  find  no  difficulty  in  the  solution 
of  this  and  some  of  the  following  problems. 

Rule .  Bring  the  place  to  the  graduated  side 
of  the  strong  brass  meridian,  and  the  degree 
which  is  over  it  is  the  latitude.  Thus  London 
will  be  found  to  have  51  deg.  30  min.  north 
latitude;  Constantinople  41  deg.  north  latitude; 
and  the  Cape  of  Good  Hope  34  deg.  south 
latitude. 

PROBLEM  VII. 

To  find  all  those  places  which  have  the  same  lati¬ 
tude  with  any  given  place. 

Suppose  the  given  place  to  be  London  ;  turn 
the  globe  round,  and  all  those  places  which  pass 
under  the  same  point  of  the  strong  brass  meri¬ 
dian,  are  in  the  same  latitude. 

F  227 


42 


DESCRIPTION  AND  USE 


PROBLEM  VIII. 

To  find  the  difference  of  latitude  between  two 

Rule .  If  the  places  be  in  the  same  hemis¬ 
phere,  bring  each  of  them  to  the  meridian,  and 
subtract  the  latitude  of  one  from  the  other.  If 
they  are  in  different  hemispheres,  add  the  lati¬ 
tude  of  one  to  that  of  the  other. 

Example .  The  latitude  of  London  is  51  deg. 
52  min.;  that  of  Constantinople  41  deg. ;  their 
difference  is  10  deg.  52  min.  The  difference  be¬ 
tween  London,  51  deg.  32  min.  north,  and  the 
Cape  of  Good  Hope,  34  deg.  south,  is  84  deg. 
32  min. 

PROBLEM  IX. 

<  ”  r  .  '■ »  - 

The  latitude  and  longitude  of  any  place  being  known , 
to  find  that  place  upon  the  globe . 

Rule .  Seek  for  the  given  longitude  in  the 
equator,  and  bring  the  moveable  meridian  to 
that  point ;  then  count  from  the  equator  on  the 
meridian,  the  degree  of  latitude  either  towards 
the  north  or  south  pole,  and  bring  the  artificial 
horizon  to  that  degree,  and  the  intersection  of 
it’s  edge  with  the  meridian  is  the  situation  re¬ 
quired. 

By  this  problem  any  place  not  represented 
on  the  globe  may  be  laid  down  thereon,  and 

228 


OF  THE  GLOBES. 


43 


it  may  be  seen  where  a  ship  is  when  it’s  latitude 
and  longitude  are  known. 

Example .  The  latitude  of  Smyrna,  in  Asia, 
is  38  deg.  28  min.  north  ;  it’s  longitude  27  deg. 
30  min.  east  of  London  ;  therefore,  bring  27  deg. 
30  min.  counted  eastward  on  the  equator,  to  the 
moveable  meridian,  and  slide  the  diameter  of 
the  artificial  horizon  to  38  deg.  28  min.  north 
latitude,  and  it’s  center  will  be  correctly  placed 
over  Smyrna. 

It  may  be  proper  in  this  place  just  to  shew 
the  pupil,  that  the  latitude  of  any  place  is  always 
equal  to  the  elevation  of  the  pole  of  the  same  place 
above  the  horizon .  The  reason  of  this  is,  that 
from  the  equator  to  the  pole  are  90  degrees, 
from  the  zenith  to  the  horizon  are  also  90 
degrees  ;  the  distance  of  the  zenith  to  the  pole 
is  common  to  both,  and  therefore  if  taken 
away  from  both,  must  leave  equal  remains ;  that 
is,  the  distance  from  the  equator  to  the  zenith, 
which  is  the  latitude,  is  equal  to  the  elevation  of 
the  pole. 

i 

OF  FINDING  THE  LONGITUDE. 

As  the  finding  the  longitude  of  places  forms 
one  of  the  most  important  problems  in  geogra¬ 
phy  and  astronomy,  some  further  account  of  it, 
it  is  presumed,  will  prove  entertaining  and  use¬ 
ful  to  the  reader. 


229 


^4  description  and  use 

<c  For  what  can  be  more  interesting  to  a 
person  in  a  long  voyage,  than  to  be  able  to  tell 
upon  what  part  of  the  globe  he  is,  to  know  howr 
far  he  has  travelled,  what  distance  he  has  to  go, 
and  how  he  must  direct  his  course  to  arrive  at 
the  place  he  designs  to  visit  ?  These  important 
particulars  are  all  determined  by  knowing  the 
latitude  and  longitude  of  the  place  under  con¬ 
sideration.  When  the  discovery  of  the  com¬ 
pass  invited  the  voyager  to  quit  his  native  shore, 
and  venture  himself  upon  an  unknown  ocean, 
that  knowledge,  which  before  he  deemed  of  no 
importance,  now  became  a  matter  of  absolute 
necessity.  Floating  in  a  frail' vessel,  upon  an 
uncertain  abyss,  he  has  consigned  himself  to  the 
mercy  of  the  winds  and  waves,  and  knows  not 
where  he  is.”* 

The  following  instance  will  prove  of  what 
use  it  is  to  know  the  longitude  of  places  at  sea. 
The  editor  of  Lord  Anson’s  voyage,  speaking 
of  the  island  of  Julian  Fernandez,  adds,  «  The 
uncertainty  we  were  in  of  it’s  position,  and  our 
standing  in  for  the  main  on  the  28th  of  May, 
in  order  to  secure  a  sufficient  easting,  when  we 
were  indeed  extremely  near  it,  cost  us  the  lives 
of  between  70  and  80  of  our  men,  by  our 
longer  continuance  at  sea;  from  which  fatal 
accident  we  might  have  been  exempted,  had 

*  Bonnycastle’s  Astronomy. 

230 


OF  THE  GLOBES. 


45 


we  been  furnished  with  such  an  account  of  it’s 
situation,  as  we  could  fully  have  depended  on.” 

The  latitude  of  a  place  the  sailor  can  easily 
discover ;  but  the  longitude  is  a  subject  of  the 
ytmost  difficulty,  for  the  discovery  of  which 
many  methods  have  been  devised.  It  is  indeed 
of  so  great  consequence,  that  the  Parliament  of 
Great  Britain  proposed  a  reward  of  10,000/.  if 
it  extended  only  to  1  degree  of  a  great  circle, 
or  60  geographical  miles  ;  1 5,000  /.  if  found  to 
40  such  miles ;  and  20,000  /.  to  the  person  that 
can  find  it  within  30  minutes  of  a  great  circle,  or 
30  geographical  miles. 

As  I  cannot  enter  fully  into  this  subject  in 
these  essays,  it  will,  I  hope,  be  deemed  sufficient, 
if  I  give  such  an  account  as  will  enable  the  reader 
to  form  a  general  idea  of  the  solution  of  this  im¬ 
portant  problem. 

From  what  has  been  seen  in  the  preceding 
pages,  it  is  evident  that  15  degrees  in  longitude 
answer  to  one  hour  in  time,  and  consequently 
that  the  longitude  of  any  place  would  be  known, 
if  we  knew  their  difference  in  time ;  or  in  other 
words,  how  much  sooner  the  sun,  &c.  arrives  at 
the  meridian  of  one  place,  than  that  of  another, 
The  hours  and  degrees  being  in  this  respect 
commensurate,  it  is  as  proper  to  express  the  dis¬ 
tance  of  any  place  in  time  as  in  degrees. 

231 


4G 


DESCRIPTION  AND  USE 


Now  it  is  clear,  that  this  difference  in  time 
would  be  easily  ascertained  by  the  observation 
of  any  instantaneous  appearance  in  the  heavens, 
at  two  distant  places  ;  for  the  difference  in  time 
at  which  the  same  phenomenon  is  observed,  will 
be  the  distance  of  the  two  places  from  each  other 
in  longitude.  On  this  principle,  most  of  the 
methods  in  general  use  are  founded. 

Thus  if  a  clock,  or  watch,  was  so  contrived, 
as  to  go  uniformly  in  all  seasons,  and  in  all 
places;  such  a  w^atch  being  regulated  to  Lon¬ 
don  time,  would  always  shew  the  time  of  the 
day  at  London  ;  then  the  time  of  the  day  under 
any  other  meridian  being  found,  the  difference 
between  that  time,  and  the  corresponding  Lon¬ 
don  time,  would  give  the  difference  in  longi¬ 
tude. 

For  supposing  any  person  possessed  of  one  of 
these  time-pieces,  to  set  out  on  a  journey  from 
London,  if  his  time  piece  be  accurately  adjust¬ 
ed,  wherever  he  is,  he  will  always  know  the 
hour  at  London  exactly ;  and  when  he  has  pro¬ 
ceeded  so  far  either  eastward  or  westward,  that 
a  difference  is  perceived  betwixt  the  hour 
shewn  by  his  time-piece,  and  those  of  the 
clocks  and  watches  at  the  places  to  which  he 
goes,  the  distance  of  those  places  from  London 
in  longitude  will  be  known.  But  to  whatever 
degree  of  perfection  such  movements  may  be 


OF  THE  GLOBES. 


4-7 


made,  yet  as  every  mechanical  instrument  is 
liable  to  be  injured  by  various  accidents,  other 
methods  are  obliged  to  be  used,  as  the  eclipses 
of  the  sun  and  moon,  or  of  Jupiter’s  satellites. 
Thus  supposing  the  moment  of  the  beginning 
of  an  eclipse  was  at  ten  o’clock  at  night  at 
London,  and  by  accounts  from  two  observers 
in  two  other  places,  it  appears  that  it  began  with 
one  of  them  at  nine  o’clock,  and  with  the  other 
at  midnight ;  it  is  plain,  that  the  place  where  it 
began  at  nine  is  one  hour,  or  15  degrees  east  in 
longitude  from  London  ;  the  other  place  where 
it  began  at  midnight,  is  30  degrees  distant  in 
west  longitude  from  London.  Eclipses  of  the 
sun  and  moon  do  not,  however,  happen  often 
enough  to  answer  the  purposes  of  navigation  ; 
and  the  motion  of  a  ship  at  sea  prevents  the  ob¬ 
servations  of  those  of  Jupiter’s  satellites. 

If  the  place  of  any  celestial  body  be  com¬ 
puted,  for  example,  as  in  an  almanack,  for  every 
day  or  to  parts  of  days,  to  any  given  meridian, 
and  the  place  of  this  celestial  body  can  be  found 
by  observation  at  sea,  the  difference  of  time 
between  the  time  of  observation  and  the  com¬ 
puted  time,  will  be  the  difference  of  longitude 
in  time.  The  moon  is  found  to  be  the  most 
proper  celestial  object,  and  the  observations  oi 
her  appulses  to  any  fixed  star  is  reckoned  one 
of  the  best  methods  for  resolving  this  difficult 
problem. 


233 


48 


description  and  use 


LENGTH  OF  THE  DEGREES  OF  LONGITUDE. 

Supposing  the  earfh  to  be  a  perfect  globe, 
the  length  of  a  degree  upon  the  meridian  has 
been  estimated  to  be  69,1  miles  ;  but  as  the 
earth  is  an  oblate  spheroid,  the  length  of  a  degree 
on  the  equator  will  be  somewhat  greater. 

Whether  the  earth  be  considered  as  a  sphe¬ 
roid  or  a  globe,  all  'the  meridians  intersect  one 
another  at  the  poles.  Therefore,  the  number 
of  miles  in  a  degree  must  always  decrease  as 
you  go  north  or  south  from  the  equator.  This 
is  evident  by  inspection  of  a  globe,  where  the 
parallels  of  latitude  are  found  to  be  smaller  in 
proportion  as  they  are  nearer  the  pole.  Hence 
it  is  that  a  degree  of  longitude  is  no  where  the 
same,  but  upon  the  same  parallel  ;  and  that  a 
degree  of  longitude  is  equal  to  a  degree  of  lati¬ 
tude  only  upon  the  equator. 

The  following  table  shews  how  many  geogra¬ 
phical  miles,  and  decimal  parts  of  a  mile,  would 
be  contained  in  a  degree  of  longitude,  at  each 
degree  of  latitude  from  the  equator  to  the  poles, 
if  the  earth  was  a  perfect  sphere,  and  the  cir¬ 
cumference  of  it’s  equinoctial  line  360  degrees, 
and  each  degree  60  geographical  miles. 

T1  lis  table  enables  us  to  determine  the  velo¬ 
city  with  which  places  upon  the  globe  revolve 

234 


OF  THE  GLOBES. 


49 


eastward  ;  for  the  velocity  is  different,  accord¬ 
ing  to  the  distance  of  the  places  from  the  equa¬ 
tor,  being  swiftest  as  passing  through  a  greater 
space,  and  so  by  degrees  slower  towards  the 
pole,  as  passing  through  a  less  space  in  the  same 
time.  Now  as  every  part  of  the  earth  is  moved 
through  the  space  of  it’s  circumference,  or  360 
degrees,  in  24  hours ;  the  space  described  in 
one  hour  is  found  by  deviding  360  by  24,  which 
gives  in  the  quotient  ]  5  degrees  ;  and  so  many 
degrees  does  every  place  on  the  earth  move  in 
an  hour.  The  number  of  miles  contained  in  so 
many  degrees  in  any  latitude,  is  readily  found 
from  the  table. 

Thus  under  the  equator  places  revolve  at  the 
rate  of  more  than  1000  miles  in  an  hour  ;  at 
London,  at  the  rate  of  about  640  miles  in  an 
hour. 


T 

ABLE, 

LAT. 

LAT. 

LAT. 

Deg.  Miles . 

Deg.  Miles . 

Deg.  Miles . 

00 

60,00 

10 

59,08 

20 

56,38 

1 

59,99 

11 

58,89 

21 

56,01 

2 

59,96 

12 

58,68 

22 

55,63 

3 

59,92 

13 

58,46 

23 

55,23 

4 

59,86 

14 

58,22 

24 

54,81 

5 

59,77 

15 

57,95 

25 

54,38 

6 

59,67 

16 

57,67 

26 

53,93 

7 

59,56 

17 

57,37 

27 

53,46 

8 

59,42 

18 

57,06 

28 

52,97 

9. 

59,26 

19 

56,73 

29 

52,47. 

G  235 


DESCRIPTION  AND  USE 


50 


Deg.  Miles . 

Deg.  Miles . 

Deg .  Miles. 

30 

51,96 

51 

37,76 

72 

18,55 

31 

5 1 ,43 

52 

36,94 

73 

17,54 

32 

50,88 

53 

36,11 

74 

16,53 

33 

50,32 

54 

35,26 

75 

15,52 

34 

49,74 

55 

34,41 

76 

14,51 

35 

49,15 

56 

33,55 

77 

13,50 

36 

48,54 

57 

32,68 

78 

12,47 

37 

47,92 

58 

31,79 

79 

11,45 

38 

47,28 

59 

30,90 

80 

10,42 

39 

46,62 

60 

30,00 

81 

9,38 

40 

45,95 

61 

29,09 

82 

8,35 

41 

45,28 

62 

28,17 

83 

7,32 

42 

44,59 

63 

27,24 . 

84 

6,28 

43 

43,88 

64 

26.30 

85 

5,23 

44 

43,16 

65 

25,36 

86 

4,18 

45 

42,43 

66 

24,41 

87 

3,14 

46 

41,68 

67 

23,45 

88 

2,09 

47 

40,92 

68 

22,48 

89 

1,05 

48 

40,15 

69 

21,50 

90 

0,00 

49 

39,36 

70 

20,52 

50 

38,57 

71 

19,54 

Another  circumstance  which  arises  from  this 
difference  of  meridians  in  time,  must  detain  us 
a  little  before  we  quit  this  subject.  For  from 
this  difference  it  follows,  that  if  a  ship  sails 
round  the  world,  always  directing  her  course 
eastward,  she  will  at  her  return  home  find  she 
has  gained  one  whole  day  of  those  that  stayed  at 
home  ;  that  is,  if  they  reckon  it  May  1 ,  the  ship’s 
company  will  reckon  it  May  2 ;  if  westward,  a 
day  less,  or  April  30. 

236 


OF  THE  GLOBES. 


51 


This  circumstance  has  been  taken  notice  of 
by  navigators.  It  was  during  our  stay  at 
Mindanao,  (says  Capt.  Dampier)  that  we  were 
first  made  sensible  of  the  change  of  time  in  the 
course  of  our  voyage  :  for  having  travelled  so 
far  westward,  keeping  the  same  course  with  the 
sun,  we  consequently  have  gained  something 
insensibly  in  the  length  of  the  particular  days, 
but  have  lost  in  the  tale  the  bulk  or  number  of 
the  days  or  hours. 

cc  According  to  the  different  longitudes  of 
England  and  Mindanao,  this  isle  being  about 
210  degrees  west  from  the  Lizard,  the  differ¬ 
ence  of  time  at  our  arrival  at  Mindanao  ought 
to  have  been  about  fourteen  hours  ;  and  so 
much  we  should  have  anticipated  our  reckon¬ 
ing,  have  gained  it  by  bearing  the  sun  com¬ 
pany. 

<c  Now  the  natural  day  in  every  place  must 
be  consonant  to  itself ;  but  going  about  with, 
or  against  the  sun’s  course,  will  of  necessity 
make  a  difference  in  the  calculation  of  the  civil 
day,  between  any  two  places.  Accordingly,  at 
Mindanao,  and  other  places  in  the  East  Indies, 
we  found  both  natives  and  Europeans  reckoning 
a  day  before  11s.  For  the  Europeans  coming 
eastward,  by  the  Cape  of  Good  Hope,  in  a 
course  contrary  to  the  sun  and  us,  wherever  we 
met,  were  a  full  day  before  us  in  their  ac¬ 
counts. 


237 


52 


DESCRIPTION  AND  USE 


“So  among  the  Indian  Mahometans,  their 
Friday  was  Thursday  with  us ;  though  it  was 
Friday  also  with  those  that  came  eastward  from 
Europe. 

“  Yet  at  the  Ladrone  islands  we  found  the 
Spaniards  of  Guam  keeping  the  same  compu¬ 
tation  with  ourselves ;  the  reason  of  which  I 
take  to  be,  that  they  settled  that  colony  by  a 
course  westward  from  Spain ;  the  Spaniards 
going  first  to  America  and  thence  to  the  La- 
drone  islands.” 

It  is  clear,  from  what  has  been  said  in  the 
first  part  of  this  article,  concerning  both  latitude 
and  longitude,  that  if  a  person  travel  ever  so  far 
directly  towards  east  or  west,  his  latitude  would 
be  always  the  same,  though  his  longitude  would 
be  continually  changing. 

But  if  he  went  directly  north  or  south,  his 
longitude  would  continue  the  same,  but  his 
latitude  would  be  perpetually  varying. 

If  he  went  obliquely,  he  would  change  both 
his  latitude  and  longitude. 

The  longitude  and  latitude  of  places  give 
only  their  relative  distances  on  the  globe;  to 
discover,  therefore,  their  real  distance,  we  have 
recourse  to  the  following  problem. 

238 


OF  THE  GLOBES. 


PROBLEM  X. 


Any  place  being  given ,  to  Jind  the  distance  of  that 
place  from  another ,  in  a  great  circle  of  the 
earth . 

I  shall  divide  this  problem  into  three  cases. 
Case  1.  If  the  places  lie  under  the  same  me¬ 
ridian.  Bring  them  up  to  the  meridian,  and 
mark  the  number  of  degrees  intercepted  be¬ 
tween  them.  Multiply  the  number  of  degrees 
thus  found  by  60,  and  they  will  give  the  num¬ 
ber  of  geographical  miles  between  the  two 
places.  But  if  we  would  have  the  number  of 
English  miles,  the  degrees  before  found  must  be 
multiplied  by  69|. 

Case  2.  If  the  places  lie  under  the  equator. 
Find  their  difference  of  longitude  in  degrees, 
and  multiply,  as  in  the  preceding  case,  by 
60  or  69 

Case  3.  If  the  places  lie  neither  under  the 
same  meridian,  nor  under  the  equator.  Then 
lay  the  quadrant  of  altitude  over  the  two  places, 
and  mark  the  number  of  degrees  intercepted 
between  them.  These  degrees  multiplied  as 
above  mentioned,  will  give  the  required  dis¬ 
tance. 


239 


.54 


DESCRIPTION  AND  USE 


PROBLEM  XI. 

To  find  the  angle  of  position  of  places . 

The  angle  of  position  is  that  formed  between 
the  meridian  of  one  of  the  places,  and  a  great 
circle  passing  through  the  other  place. 

Rectify  the  globe  to  the  latitude  and  zenith 
of  one  of  the  places,  bring  that  place  to  the 
strong  brass  meridian,  set  the  graduated  edge 
of  the  quadrant  to  the  other  place,  and  the 
number  of  degrees  contained  between  it  and  the 
strong  brass  meridian,  is  the  measure  of  the 
angle  sought.  Thus, 

The  angle  of  position  between  the  meridian 
of  Cape  Clear,  in  Ireland,  and  St.  Augustine,  in 
Florida,  is  about  82  degrees  south  westerly  ;  but 
the  angle  of  position  between  St.  Augustine  and 
Cape  Clear,  is  only  about  46  degrees  north 
easterly. 

Hence  it  is  plain,  that  the  line  of  position,  or 
azimuth,  is  not  the  same  from  either  place  to 
the  other,  as  the  romb-line  are. 

PROBLEM  XII. 

To  find  the  bearing  of  one  place  from  another , 

The  bearing  of  one  sea-port  from  another 
is  determined  by  a  kind  of  spiral,  called  a 
romb-line,  passing  from  one  to  the  other,  so  as 

240 


OF  THE  GLOBES. 


55 


to  make  equal  angles  with  all  the  meridians  it 
passes  by ;  therefore,  if  both  places  are  situated 
on  the  same  parallel  of  latitude,  their  bearing  is 
either  east  or  west  from  each  other ;  if  they  are 
upon  the  same  meridian,  they  bear  north  and 
south  from  one  another;  if  they  lie  upon  a  romb- 
line,  their  bearing  is  the  same  with  it ;  if  they 
do  not,  observe  to  which  romb-line  the  two 
places  are  nearest  parallel,  and  that  will  shew 
the  bearing  sought. 

Example .  Thus  the  bearing  of  the  Lizard 
point  from  the  island  of  Bermudas  is  nearly 
E.  N.  E. ;  and  that  of  Bermudas  from  rhe 
Lizard  is  W.  S.  W.  both  nearly  upon  the  same 
romb-line,  but  in  contrary  directions. 


OF  THE  TWILIGHT. 

That  light  which  we  have  from  the  sun  be¬ 
fore  it  rises,  and  after  it  sets,  is  called  the  twi¬ 
light. 

The  morning  twilight,  or  day  break,  com¬ 
mences  when  the  sun  comes  within  eighteen  de¬ 
grees  of  the  horizon,  and  continues  till  sun- 
rising.  The  evening  twilight  begins  at  sun¬ 
setting,  and  continues  till  it  is  eighteen  degrees 
below  the  horizon. 

To  illustrate  the  causes  of  the  various  length 
of  twilight  in  different  places,  a  wire  circle  is 
fixed  eighteen  degrees  below  the  surface  of  the 

241 


.36 


description  and  use 


broad  paper  circle ;  so  that  all  those  places 
which  are  above  the  wire  circle  will  have  twi¬ 
light,  but  it  will  be  dark  to  all  those  places  be¬ 
low  it. 

I  have  already  observed,  that  it  is  owing  to 
the  atmosphere  that  we  are  favoured  with  the 
light  of  the  sun  before  he  is  above,  and  after  he 
is  below,  our  horizon.  Hence,  though  after 
sun-setting  we  receive  no  direct  light  from  the 
sun,  yet  we  enjoy  his  reflected  light  for  some 
time ;  so  that  the  darkness  of  the  night  does  not 
come  on  suddenly,  but  by  degrees. 

In  a  right  position  of  the  sphere  the  twilights 
are  quickly  over,  because  the  sun  rises  and  sets 
nearly  in  a  perpendicular ;  but  in  an  oblique 
sphere  they  last  longer,  the  sun  rising  and  set¬ 
ting  obliquely.  The  greater  the  latitude  of  the 
place,  the  longer  is  the  duration  of  the  twilight; 
so  that  all  those  who  are  in  49  degrees  of  lati¬ 
tude  have  in  the  summer,  near  the  solstice,  their 
atmosphere  enlightened  the  whole  night,  the  twi¬ 
light  lasting  till  sun-rising. 

In  a  parallel  sphere,  the  twilight  lasts  for 
several  months ;  so  that  the  inhabitants  of  this 
position  have  either  direct  or  reflex  light  of  the 
sun  nearly  all  the  year,  as  will  plainly  appear  by 
the  globe. 


242 


OF  THE  GLOBES. 


57 


OF  THE  DIURNAL  MOTION  OF  THE  EARTH, 
AND  THE  PROBLEMS  DEPENDING  ON  THAT 
MOTION. 


As  the  daily  motion  of  the  earth  about  it’s 
axis,  and  the  phenomena  dependent  on  it,  are 
some  of  the  most  essential  points  which  a  begin¬ 
ner  ought  to  have  in  view,  we  shall  now  endea¬ 
vour  to  explain  them  by  the  globes  ;  and  here  I 
think  the  advantage  of  globes  mounted  in  my 
father’s  manner,  over  those  generally  used,  will 
be  very  evident. 

I  have  already  observed,  that  in  globes  mount¬ 
ed  in  our  manner,  the  motion  of  the  terrestrial 
globe  about  it’s  axis  represents  the  diurnal 
motion  of  the  earth,  and  that  the  horary  index 
will  point  out  upon  the  equator  the  24  hours  of 
one  diurnal  rotation,  or  any  part  of  that  time. 

I  shall  now  consider  the  broad  paper  circle  as 
the  plane  which  distinguishes  light  from  darkness  ; 
that  is,  the  enlightened  half  of  the  earth’s  sur¬ 
face,  from  that  which  is  not  enlightened. 

For  when  the  sun  shines  upon  a  globe,  he 
shines  only  upon  one  half  of  it ;  that  is,  one  half 
of  the  globe’s  surface  is  enlightened  by  him,  the 
other  not. 

That  the  enlightened  half  may  be  that  half 

H  243 


58 


description  and  use 


which  is  above  the  broad  paper  circle,  we  must 
imagine  the  sun  to  be  in  our  zenith . 

Or  let  a  sun  be  painted  on  the  ceiling  over 
the  terrestrial  globe,  the  diameter  of  the  picture 
equal  to  the  diameter  of  the  globe. 

Then  all  those  places  that  are  above  the 
broad  paper  circle  will  be  in  the  sun’s  light ;  that 
is,  it  will  be  day  in  all  those  places. 

And  all  places  that  are  below  this  circle,  will 
be  out  of  the  sun’s  light ;  that  is,  in  all  those 
places  it  will  be  night . 

When  any  place  on  the  earth’s  surface  comes 
to  the  edge  of  the  broad  paper  circle,  passing 
out  of  the  shade  into  the  light,  the  sun  will  ap¬ 
pear  rising  at  that  place. 

And  when  a  place  is  at  the  edge  of  the  broad 
paper  circle,  going  out  of  the  light  into  the 
shade,  the  sun  will  appear  at  that  place  to  be 
setting . 

When  wre  view  the  globe  in  this  position,  we 
at  once  see  the  situation  of  all  places  in  the  illu¬ 
minated  hemisphere,  whose  inhabitants  enjoy  the 
light  of  the  day.  One  edge  of  the  broad  paper 
circle  shews  at  what  place  the  sun  appears 
rising  at  the  same  time ;  and  the  opposite  edge 
shews  at  what  places  the  sun  is  setting  at  the 
same  time. 

The  horary  index  shews  how  long  a  place 
is  moving  from  one  edge  to  the  other ;  that  is, 
how  long  the  day  or  night  is  at  that  place- 

244 


OF  THE  GLOBES, 


59 


and,  consequently,  when  the  globe  is  thus  situ¬ 
ated,  you  readily  discover  the  time  of  the  sun's 
rising  and  setting  on  any  given  day,  in  any  given 
place. 


TO  RECTIFY  THE  TERRESTRIAL  GLOBE. 

To  rectify  the  terrestrial  globe,  is  to  place  it 
in  the  same  position  in  which  our  earth  stands  to 
the  sun,  at  all  or  at  any  given  times. 

That  half  of  the  earth's  surface  which  is  en¬ 
lightened  by  the  sun  is  not  always  the  same ;  it 
differs  according  as  the  sun’s  declination  differs. 

To  rectify,  then,  the  terrestrial  globe,  is  to 
bring  it  into  such  a  position,  as  that  the  enlight¬ 
ened  half  of  the  earth’s  surface  may  be  all  above 
the  broad  paper  circle.  * 

On  the  back  side  of  the  strong  brass  meridian, 
and  on  each  side  of  the  north  pole,  the  months 
and  days  of  the  month  are  graduated  in  two 
concentric  spaces,  agreeable  ta  the  declination  of 
the  sun. 

Bring  the  day  of  the  month  that  is  graduated 
on  the  back  side  of  the  strong  brass  meridian, 
to  coincide  with  the  broad  paper  circle,  and  the 
globe  is  rectified.  1 

Thus  set  the  first  of  May  to  coincide  with 
the  broad  paper  circle,  and  that  half  of  the 
earth’s  surface  which  is  enlightened  at  any 

245 


CjO 


DESCRIPTION  AND  USE 


time  upon  that  day,  will  be  all  at  once  above 
the  said  circle. 

If  the  horary  index  be  set  to  XII,  when  any 
particular  place  is  brought  under  the  strong 
brass  meridian,  it  will  shew  the  precise  time  of 
sun-rising  and  sun-setting  at  that  place,  accord¬ 
ing  as  that  place  is  brought  to  the  eastern  or 
western  edge  of  the  broad  paper  circle. 

It  will  also  shew  how  long  any  place  is  in 
moving  from  the  east  to  the  west  side  of  the 
illuminated  disk,  and  thence  the  length  of  the 
day  and  night. 

It  will  also  point  out  the  length  of  the  twi¬ 
light,  by  shewing  the  time  in  which  the  place  is 
passing  from  the  twilight  circle  to  the  edge  of 
the  broad  paper  circle  on  the  western  side ;  or 
from  the  edge  of  this  circle  on  the  eastern  side, 
to  the  twilight  wire,  and  thus  determine  the 
length  of  the  whole  artificial  day. 

N.  B.  The  twilight  wire  is  placed  at  18  de¬ 
grees  from  the  broad  paper  circle. 

I  shall  now  proceed  to  exemplify  upon  the 
globes  these  particulars,  at  three  different  sea¬ 
sons  of  the  year,  viz.  the  summer  solstice,  the 
winter  solstice,  and  the  time  or  times  of  the 
equinoxes. 


246 


OF  THE  GLOBES 


1)1 


PROBLEM  XIII. 

/  v 

To  place  the  globe  in  the  same  situation ,  with  respect 
to  the  sun ,  as  our  earth  is  in  at  the  time  of  the 
SUMMER  SOLSTICE. 

Rectify  the  globe  to  the  extremity  of  the  di¬ 
visions  for  the  month  of  June,  or  23 1  degrees 
north  declination  ;  that  is,  bring  these  divisions 
on  the  strong  brass  meridian  to  coincide  with 
the  plane  of  the  broad  paper  circle. 

Then  that  part  of  the  earth’s  surface,  which 
is  within  the  northern  polar  circle,  will  be  above 
the  broad  paper  circle,  and  will  be  in  the  light, 
and  the  inhabitants  thereof  will  have  no  night. 

But  all  that  space  which  is  contained  within 
the  southern  polar  circle,  will  continue  in  the 
shade ;  that  is,  it  will  there  be  continual 
night. 

In  this  position  of  the  globe,  the  pupil  will 
observe  how  much  the  diurnal  arches  of  the  pa¬ 
rallels  of  latitude  decrease,  as  they  are  more  and 
more  distant  from  the  elevated  pole. 

If  any  place  be  brought  under  the  strong 
brass  meridian,  and  the  horary  index  is  set  to 
that  XII  which  is  most  elevated,  and  the  place 
be  afterwards  brought  to  the  western  side  of 
the  broad  paper  circle,  the  hour  index  will 

shew  the  time  of  sun-rising  ;  and  when  the 

247 


62 


DESCRIPTION  AND  USE 


place  is  moved  to  the  eastern  edge,  the  index 
points  to  the  time  of  sun-setting. 

✓ 

The  length  of  the  day  is  obtained  by  the  time 
shewn  by  the  horary  index,  while  the  globe 
moves  from  the  west  to  the  east  side  of  the  broad 
paper  circle. 

Thus  it  will  be  found,  that  at  London  the  sun 
rises  about  15  minutes  before  IV  in  the  morning, 
and  sets  about  1 5  minutes  after  VIII  at  night. 


At  the  following  places  it  will  be  nearly  at  the 
times  expressed  in  the  table. 


* 

O 

O 

Length 

1  Twi¬ 

Rising. 

Setting. 

of  day. 

light. 

» 

/;.  in. 

h.  m. 

h.  m • 

h.  m. 

Cape  Horn 

8  44 

3  16 

6  32 

2  35 

Cape  of  Good  Hope 

7  9 

4  51 

9  42 

1  43 

Rio  de  Janeiro,  in  Brazil 

6  42 

5  19 

10  38 

l  23 

Island  of  St.  Thomas’s  near 
the  equator. 

6 

6 

12 

1  20 

Cape  Lucas,  California 

5  12| 

6  48 

13  36 

1  35 

We  also  see,  that  at  the  same  time  the  sun  is 
rising  at  London,  it  is  rising  at  the  isles  of  Si¬ 
cily  and  Madagascar. 

And,  that  at  the  same  time  when  the  sun  sets 
at  London  it  is  setting  at  the  island  of  Madeira, 
and  at  Cape  Horn. 

And  when  the  sun  is  setting  at  the  island  of 
Borneo,  in  the  East  Indies,  it  is  rising  at  Flo¬ 
rida,  in  America.  And  many  other  similar 

248 


OF  THE  GLOBES* 


63 

circumstances  relative  to  other  places,  are  seen 
as  it  were  by  inspection. 


PROBLEM  XIV. 

To  explain  the  situation  of  the  earthy  with  re - 

spect  to  the  sun ,  at  the  tune  of  the  winter 

SOLSTICE. 

Rectify  the  globe  to  the  extremity  of  the  di¬ 
visions  for  the  month  of  December,  or  to  23} 
degrees  south  declination. 

When  it  will  be  apparent  that  the  whole  space 
within  the  southern  polar  circle  is  in  the  sun’s 
light,  and  enjoys  continual  day ;  whilst  that  of 
the  northern  polar  circle  is  in  the  shade,  and  has 
continual  night. 

If  the  globe  be  turned  round,  as  before,  the 
horary  index  will  shew,  that  at  the  several  places 
before-mentioned  their  days  will  be  respectively 
equal  to  what  their  nights  were  at  the  time  of 
the  summer  solstice. 

It  will  appear  farther,  that  it  is  now  sun-set- 
ting  at  the  same  time  in  those  places  in  which  it 
was  sun-rising  at  the  same  time  at  the  summer 
solstice  ;  and,  on  the  contrary,  sun-rising  at  the 
time  it  then  appeared  to  set. 

249 


64 


DESCRIPTION  AND  USE 


PROBLEM.  XV. 

To  place  the  globe  in  the  situation  of  the  earthy  at 
the  times  of  the  equinox. 

The  sun  has  no  declination  at  the  times  of  the 
equinox,  consequently  there  must  be  no  eleva¬ 
tion  of  the  pole. 

Bring  the  day  of  the  month  when  the  sun  en¬ 
ters  the  first  point  of  Aries,  or  day  of  the  month 
when  the  sun  enters  the  first  point  of  Libra,  to 
•  the  plane  of  the  broad  paper  circle ;  then  the 
two  poles  of  the  globe  will  be  in  that  plane  also, 
and  the  globe  will  be  in  the  position  which  is 
called  a  right  sphere . 

For  it  is  a  right  sphere  when  the  two  poles 
are  in  the  plane  of  the  broad  paper  circle,  be¬ 
cause  then  all  those  circles  which  are  parallel  to 
the  equator  will  be  at  right  angles  to  that  plane. 

If  the  globe  be  now  turned  from  west  to  east, 
it  will  plainly  appear,  that  all  places  upon  it’s 
surface  are  twelve  hours  above  the  broad  paper 
circle,  and  twelve  hours  below  it ;  that  is,  the 
days  are  twelve  hours  long  all  over  the  earth, 
and  the  nights  are  equal  to  the  days,  whence 
these  times  are  called  the  times  of  equinox. 

Two  of  these  occur  in  every  year  ;  the  first 

250 


OF  THE  GLOBES. 


65 


is  the  autumnal,  the  second  the  vernal  equi¬ 
nox. 

At  these  seasons  the  sun  appears  to  rise  at  the 
same  time  to  all  places  that  are  on  the  same  me¬ 
ridian.  The  sun  sets  also  at  the  same  time  in  all 
those  places. 

Thus  if  London  and  Mundford,  on  the  gold 
coast,  be  brought  to  the  strong  brass  meridian, 
the  graduated  side  of  which  is  in  this  case  the 
horary  index,  and  they  be  afterwards  carried  to 
the  western  edge  of  the  broad  paper  circle,  the 
index  will  shew  that  the  sun  rises  at  VI  at  both 
places  ;  when  they  are  carried  to  the  eastern 
edge,  the  index  points  to  VI  for  the  time  of  sun¬ 
setting. 

N.  B.  If  London  be  not  the  given  place,  the 
hour  index  is  to  be  set  to  the  most  elevated  XII, 
while  the  place  is  under  the  graduated  edge  of 
the  strong  brass  meridian. 

The  following  circumstances,  which  usually 
attend  the  four  cardinal  divisions  of  the  year, 
cannot  be  better  introduced  than  at  this  place. 
At  the  time  of  the  equinoxes,  wheji  the  sun 
passes  from  one  hemisphere  into  the  other, 
there  is  almost  constantly  some  disturbance  in 
the  weather ;  the  winds  are  then  generally 
higher :  at  the  vernal  equinox  they  are  for  the 
most  part  easterly,  cold,  dry,  and  searching. 
The  solstitial  point  of  the  summer  is  often  dis¬ 
tinguished  by  violent  rains,  and  that  we  call 

I  25 1 


DESCRIPTION  AND  USE 


66 

a  midsummer  flood.  The  winter  being  less  rainy 
than  the  summer,  nothing  particular  happen* 
at  the  winter  solstice,  but  that  the  frosts  com¬ 
monly  set  in  more  severely,  with  some  quantity 
of  snow  upon  the  ground. 


OF  THE  ARTIFICIAL  OR  TERRESTRIAL 

HORIZON. 

The  brass  circle,  which  may  be  slipped  from 
pole  to  pole  on  the  moveable  meridian,  has 
been  already  described.  The  circumference  of 
it  is  divided  into  eight  parts,  to  which  are  affix¬ 
ed  the  initial  letters  of  the  mariner’s  compass. 

When  the  center  of  it  is  set  to  any  particular 
place,  the  situation  of  any  other  place  is  seen, 
with  respect  to  that  place ;  that  is,  whether  they 
be  east,  west,  north,  or  s  uth  of  it. 

It  will  therefore  represent  the  horizon  of  that 
place. 

We  shall  here  use  this  artificial  horizon,  to 
shew  why  the  sun,  although  he  be  always  in  one 
and  the  same  place,  appears  to  the  inhabitants 
of  the  earth  at  different  altitudes,  and  in  different 
azimuths. 


2.52 


OF  THE  GLOBES. 


g; 


PROBLEM  XVI. 

1  o  exemplify  the  sun' s  altitude ,  as  observed  with 

an  artificial  horizon. 

The  altitude  of  the  sun  is  greater  or  less,  ac¬ 
cording  as  the  line  which  goes  from  us  to  the  sun 
is  nearer  to,  or  farther  off  from  our  horizon. 

Let  the  moveable  circle  be  applied  to  any  place, 
as  London,  then  will  the  horizon  of  London  be 
thereby  represented. 

The  sun  is  supposed,  as  before,  to  be  in  the 
zenith,  that  is,  directly  over  the  terrestrial 
globe. 

If  then  from  London  a  line  go  vertically  up¬ 
wards,  the  sun  will  be  seen  at  London  in  that 
line. 

At  sun-rising,  when  London  is  brought  to  the 
west  edge  of  the  broad  paper  circle,  the  suppos¬ 
ed  line  will  be  parallel  to  the  artificial  horizon, 
and  the  sun  will  then  be  seen  in  the  horizon. 

As  the  globe  is  gradually  turned  from  the 
west  towards  the  east,  the  horizon  will  recede 
from  that  line  which  goes  from  London  verti¬ 
cally  upwards  ;  so  that  the  line  in  which  the 
sun  is  seen  gets  further  and  further  from  the 
horizon ;  that  is,  the  sun’s  altitude  increases 
gradually. 


253 


DESCRIPTION  AND  USE 


(38 

When  the  horizon,  and  the  line  which  goes 
from  London  vertically  upwards,  are  arrived  at 
the  strong  brass  meridian,  the  sun  is  then  at  his 
greatest  or  meridian  altitude  for  that  day,  and 
the  line  and  horizon  are  at  the  largest  angle 
they  can  make  with  each  other. 

After  this,  the  motion  of  the  globe  being  con¬ 
tinued,  the  angle  between  the  artificial  horizon, 
and  the  line  which  goes  from  London  vertically 
upwards,  continually  decreases,  until  London 
arrives  at  the  eastern  edge  of  the  broad  paper 
circle ;  it’s  horizon  then  becomes  vertical  again, 
and  parallel  to  the  line  which  goes  vertically  up¬ 
wards.  The  sun  wall  again  appear  in  the  hori¬ 
zon,  and  will  set. 

PROBLEM  XVII. 

Of  the  suns  meridian  altitude ,  at  the  three  differ¬ 
ent  seasons . 

Rectify  the  globe  to  the  time  of  the  winter 
solstice,  by  problem  xiv,  and  place  the  center  of 
the  visible  horizon  on  London. 

When  London  is  at  the  graduated  edge  of  the 
strong  brass  meridian,  the  line  which  goes  verti¬ 
cally  upwards  makes  an  angle  of  about  15  de¬ 
grees  ;  this  is  the  sun’s  meridian  altitude  at  that 
season,  to  the  inhabitants  of  London. 

If  the  globe  be  rectified  to  the  times  of 
equinox,  by  problem  xv,  the  horizon  will  be 

254 


OF  THE  GLOBES. 


69 


farther  separated  from  the  line  which  goes  verti¬ 
cally  Upwards,  and  makes  a  greater  angle  there¬ 
with,  it  being  about  38|  degrees  ;  this  is  the 
sun’s  meridian  altitude,  at  the  time  of  equinox 
at  London. 

Again,  rectify  to  the  summer  solstice  by 
problem  xiii,  and  you  will  find  the  artificial 
horizon  recede  farther  from  the  line  which  goes 
from  London  vertically  upwards,  and  the  angle 
it  then  makes  is  about  62  degrees,  which  shews 
the  sun’s  meridian  altitude  at  the  time  of  the 
summer  solstice. 

V 

Hence  flows  also  the  following  arithmetical 

problem. 

v  PROBLEM  XVIII. 

To  find  the  sun9 s  meridian  altitude  universally . 

Add  the  sun’s  declination  to  the  elevation  of 
the  equator,  if  the  latitude  of  the  place,  and  the 
declination  of  the  sun,  are  both  on  the  same  side. 

If  on  contrary  sides,  subtract  the  declination 
from  the  elevation  of  the  equator,  and  you  obtain 
the  sun’s  meridian  altitude. 

Thus  the  elevation  of  the  equator  at 

London  is  ...  38°  28 

The  sun’s,  declination  on  the  20th  of 

May  20  8 


Their  sum,  the  sun’s  meridian  altitude 

that  day  -  -  -  -  58  36 


70 


DESCRIPTION  AND  USE 


Again,  to  the  elevation  of  the  equator 


at  London  * 

38° 

28 

Add  the  sun’s  greatest  declination  at 

the  time  of  the  summer  solstice 

23 

29 

The  sum  is  the  sun’s  greatest  meridian 

altitude  at  London 

61 

57 

PROBLEM  XIX. 

Of  the  sun's  azimuths ,  as  compared  with  the  arti¬ 
ficial  horizon . 

The  artificial  horizon  serves  also  to  determine 
the  sun’s  azimuths. 

An  azimuth  of  the  sun  is  denominated  from 
that  point  of  the  horizon,  to  which  the  sun,  or 
a  line  going  to  the  sun,  is  nearest. 

Thus  if  the  sun,  or  a  line  going  to  the  sum 
be  nearest  the  south-east  point  of  the  horizon, 
which  point  is  45  degrees  distant  from  the  me¬ 
ridian,  the  sun’s  azimuth  is  an  azimuth  of  45 
degrees,  and  the  sun  will  appear  in  the  south¬ 
east. 

Imagine  the  sun,  as  we  have  done  before,  to 
be  placed  directly  over  the  globe. 

In  which  case,  a  line  going  to  the  sun  from 
any  place  on  the  surface  of  the  globe,  will  have 
a  vertical  direction,  and  will  go  from  that  place 
vertically  upwards. 


256 


OF  THE  GLOBES* 


71 


If  then  we  apply  the  artificial  horizon  to  any 
place,  the  point  of  this  horizon  to  which  a  verti¬ 
cal  line  is  nearest,  shews  the  sun’s  azimuth  at 
that  time. 

It  is  observable,  that  the  point  of  the  horizon 
to  which  such  a  vertical  line  is  nearest,  will  be 
at  all  times  that  point  which  is  most  elevated. 

To  exemplify  this,  let  the  globe  be  in  the 
position  of  a  right  sphere,  and  let  the  artificial 
horizon  be  applied  to  London. 

When  London  is  at  the  western  edge  of  the 
broai  paper  circle,  which  situation  represents 
the  time  when  the  sun  appears  to  rise,  the  eastern 
point  of  the  artificial  horizon  being  then  most 
elevated,  shews  that  the  sun  at  his  rising  is  due 
east. 

Turn  the  globe,  till  London  comes  to  the 
eastern  edge  of  the  broad  paper  circle,  then  the 
western  point  of  the  artificial  horizon  will  be 
most  elevated,  shewing  that  the  sun  sets  due 
west. 

Now  place  the  globe  in  the  position  of  an 
oblique  sphere ;  and  if  London  be  brought  to 
the  eastern  or  western  side  of  the  broad  paper 
circle,  the  vertical  line  will  depart  more  or  less 
from  the  east  and  west  points,  in  which  case  the 
sun  is  said  to  have  more  or  less  amplitude . 

If  the  departure  be  northward,  it  is  called 

257 


72 


DESCRIPTION  AND  USE 


northern  amplitude  ;  if  southward,  it  is  called 
southern  amplitude. 

In  whatever  position  the  globe  be  placed, * 
when  London  comes  to  the  strong  brass  meri¬ 
dian,  the  most  elevated  part  of  the  artificial 
horizon  will  be  the  south  point  of  it. 

Which  shews  that  at  noon  the  sun  will  always, 
and  in  all  seasons,  appear  in  the  south. 

OF  THE  ANCIENT  DIVISIONS  OF  THE  EARTH 
INTO  ZONES  AND  CLIMATES. 

Climates  was  a  term  used  by  the  ancient  as¬ 
tronomers  to  express  a  division  of  the  earth, 
which,  before  the  marking  down  the  latitudes  of 
countries  into  degrees  and  minutes  was  in  use, 
served  them  for  dividing  the  earth  into  certain 
portions  in  the  same  direction,  so  as  to  speak  of 
any  particular  place  with  some  degree  of  cer¬ 
tainty,  though  not  with  due  precision. 

It  was  natural  for  the  earliest  observers  to  re¬ 
mark,  for  one  of  the  first  things,  the  diversity 
that  there  was  in  the  sun’s  rising  and  setting : 
it  was  by  this  they  regulated  what  they  called 
climates ;  which  are  a  tract  on  the  surface 
of  the  earth,  of  various  breadths,  being  regu¬ 
lated  by  the  different  lengths  of  time  be- 

*  The  globe  is  not  supposed  in  this  case,  or  under  this 
view  of  things,  ever  to  be  elevated  above  the  limits  of  the. 
sun’s  declination. 


2.58 


OF  THE  GLOBES. 


73 


tween  the  rising  and  setting  of  the  sun  in  the 
longest  day,  in  different  places. 

From  the  equator  to  the  latitude  66i  north 
and  south,  a  climate  is  constituted  by  the  differ¬ 
ence  of  half  an  hour  in  the  length  of  the  longest 
day,  and  this  is  sufficient  for  understanding  the 
ancients.  Between  the  polar  circle  and  the  pole, 
the  length  of  the  longest  day,  in  one  parallel,  ex¬ 
ceeds  the  length  of  the  longest  in  the  next  by  a 
month \  but  of  these  the  ancients  knew  nothing. 


CLIMATES  BETWEEN  THE  EQUATOR  AND 

POLAR  CIRCLES. 


c/5 

V 

• 

C/5 

Latitude. 

Breadth. 

c/5 

0) 

• 

C/3 

Latitu.de, 

Breadth. 

2 

4-> 

Jh 

2 

£ 

»  rH 

u 

o 

a 

,  D.  M. 

D. 

M. 

- 

5 

o 

w 

D. 

M. 

D. 

M. 

1 

l2i 

8 

25 

.8 

25 

13 

1 8-1 

59 

58 

1 

29 

2 

13 

16 

25 

.8- 

00 

.14 

19 

61 

18 

1 

20 

3 

13'! 

23 

50 

7 

25 

'15 

19-1 

2 

62 

25 

1 

07 

4 

14 

30 

25 

6 

30 

IS 

20 

63 

22 

0 

57 

0 

144 

36 

28 

6 

08 

17 

251 

64 

06 

0 

44 

6 

15 

41 

22 

4 

54 

18 

21 

64 

49 

0 

43 

7 

15‘| 

45 

29 

4 

07 

19 

211 

65 

21 

0 

32 

8 

16 

49 

01 

.O 

O 

32 

20 

22 

55 

47 

0 

22, 

9 

*4 

52 

00 

2 

57 

2  i 

22  > 

66 

06 

0 

19 

10 

17 

54 

27 

2 

29 

22 

23 

66 

20 

0 

14 

11 

l7i 

56 

37 

2 

10 

23 

231 

66 

28 

0 

08 

12 

18 

58 

29 

1 

52 

24 

24 

66 

31 

0 

03 

Therefore,  to  discover  in  what  climate  a 
place  is,  whose  latitude  does  not  exceed  66 f 

K  250 


74 


DESCRIPTION  AND  USE 


degrees,  find  the  length  of  the  longest  day  in 
that  place,  and  subtracting  12  hours  from  that 
length,  the  number  of  half  hours  in  the  re¬ 
mainder  will  specify  the  climate. 

problem  xx. 

To  find  the  limits  of  the  climates . 

Elevate  the  north  pole  to  23°  28  ,  the  sun’s 
declination  on  the  longest  day ;  and  turn  the 
globe  easterly  till  the  intersection  of  the  meridian 
with  the  equator  that  passes  through  Libra 
comes  to  the  horizon,  and  the  hour  of  VI  will 
then  be  under  the  meridian,  which  in  this  prob¬ 
lem  is  the  hour  index,  because  the  sun  sets  this 
day  at  places  on  the  equator  as  it  does  every  day 
at  VI  o’clock.  Now  turn  the  globe  easterly  till 
the  time  under  the  meridian  is  15  min.  past  VI. 
and  you  find  that  8°  34'  of  that  graduated  meri¬ 
dian  is  cut  by  the  horizon  ;  this  is  the  beginning 
of  the  second  climate ;  and  the  limits  of  ail  the 
climates  may  be  determined,  by  bringing  succes¬ 
sively  the  time  equal  to  half  the  length  of  the 
longest  day  under  the  meridian,  and  observing 
the  degree  of  the  graduated  meridian  cut  by  the 
horizon. 

ZONES. 

Zones  is  another  division  of  the  earth’s  sur¬ 
face  used  by  the  ancients :  that  part  which  the 

260 


OF  THE  GLOBES. 


7  5 


sun  passes  over  in  a  year,  comprehending  23i 
degrees  on  each  side  the  equator,  was  called  by 
the  ancients  the  torrid  zone.  The  two  frigid 
zones  are  contained  between  the  polar  circles. 
Between  the  torrid  and  the  two  frigid  zones  are 
contained  the  two  temperate  ones*  each  being 
about  43  degrees  broad. 

The  latitude  of  a  place  being  the  mark  of  it’s 
position  with  respect  to  the  sun,  may  be  consider¬ 
ed  as  a  general  index  to  the  temperature  of  the 
climate  :  it  is,  however,  liable  to  very  great 
exceptions ;  but  to  deny  it  absolutely  would  be 
to  deny  that  the  sun  is  the  source  of  light  and 
heat  below* 

Nothing  can  be  more  hideous  or  mournful 
than  the  pictures  which  travellers  present  us  of 
the  polar  regions*  The  seas,  surrounding  in¬ 
hospitable  coasts,  are  covered  with  islands  of 
ice,  that  have  been  increasing  for  many  cen¬ 
turies  :  some  of  these  islands  are  immersed  six 
hundred  feet  under  the  surface  of  the  sea,  and 
yet  often  rear  up  also  their  icy  heads  more  than 
one  hundred  feet  above  it’s  level,  and  are  three 
or  four  miles  in  circumference.  The  follow¬ 
ing  account  will  give  some  idea  of1  the  scenery 
produced  by  arctic  weather.  At  Smearing- 
borough  Harbour,  within  fifteen  degrees  of  the 
pole,  the  country  is  full  of  mountains,  pre¬ 
cipices,  and  rocks  ;  these  are  covered  with  ice 
and  snow.  In  the  vallies  are  hills  of  ice. 

261 


76 


DESCRIPTION  AND  USE 


which  seem  daily  to  accumulate.  These  hills 
assume  many  strange  and  fantastic  appearances;, 
some  looking  like  churches  or  castles,  ruins, 
ships  in  full  sail,  whales,  monsters,  and  all  the 
various  forms  that  fill  the  universe.  There  are 
seven  of  these  ice-hills,  which  are  the  highest  in 
the  country.  When  the  air  is  clear,  and  the 
light  shines  full  upon  them,  the  prospect  is  in¬ 
conceivably  brilliant ;  the  sun  is  reflected  from 
them  as  from  glass ;  sometimes  they  appear  of 
a  bright  hue,  like  sapphire;  sometimes  varie¬ 
gated  with  all  the  glories  of  the  prismatic 
colours,  exceeding,  in  the  magnitude  of  lustre, 
and  beauty  of  colour,  the  richest  gems  in  the 
world,  disposed  in  shapes  wonderful  to  behold, 
dazzling  the  eye  with  the  brilliancy  of  it's 
splendor.  At  Spitsbergen,  within  ten  degrees 
of  the  pole,  the  earth  is  locked  up  in  ice  till  the 
middle  of  May ;  in  the  beginning  of  July  the 
plants  are  in  flower,  and  perfect  their  seeds  in  a 
month* s  time  :  for  though  the  sun  is  much  more 
oblique  in  the  higher  latitudes  than  with  us,  his 
long  continuance  above  the  horizon  is  attended 
with  an  accumulation  of  heat  exceeding  that  of 
many  places  under  the  torrid  zone ;  and  there  is 
reason  to  suppose,  that  the  rays  of  the  sun,  at 
any  given  altitude,  produce  greater  degrees  of 
heat  in  the  condensed  air  of  the  polar  regions, 
than  in  the  thinner  air  of  this  climate. 

262 


OF  THE  GLOBES. 


Yet,  if  we  look  for  heat,  and  the  remarkable  1 
effects  of  it,  we  must  go  to  the  countries  n  ar 
the  equator,  where  we  shall  find  a  scenery  totally 
different  from  that  of  the  frigid  zone.  Here  all 
things  are  upon  a  larger  scale  than  in  the  temper¬ 
ate  climates  ;  their  days  are  burning  hot ;  in 
some  parts  their  nights  are  piercing  cold  ;  their 
rains  lasting  and  impetuous,  like  torrents ;  their 
dews  excessive ;  their  thunder  and  lightning 
more  frequent,  terrible,  and  dangerous ;  the 
heat  burns  up  the  lighter  soil,  and  forms  it  into 
a  sandy  desert,  while  it  quickens  all  the  moister 
tracts  with  incredible  vegetation. 

The  ancients  supposed  that  the  frigid  zone 
was  uninhabitable  from  cold,  and  the  torrid  from 
the  intolerable  heat  of  the  sun ;  we  now,  how¬ 
ever,  know  that  both  are  inhabited.  The  senti¬ 
ments  of  the  ancients,  therefore,  in  this  respect, 
are  a  proof  how  inadequate  the  faculties  of  the 
human  mind  are  to  discussions  of  this  nature* 

when  unassisted  by  facts. 

* 

OF  THE  ANCIENT  DISTINCTION  OF  PLACES, 
BY  THE  DIVERSITY  OF  SHADOWS  OF  UP¬ 
RIGHT  BODIES  AT  NOON. 

When  the  sun  at  noon  is  in  the  zenith  of 
any  place,  the  inhabitants  of  that  place  were 
by  the  ancients  called  ascii,  that  is,  without 

263 


78 


DESCRIPTION  AND  USE 


shadow ;  for  the  shadow  of  a  man  standing  up¬ 
right,  when  the  sun  is  directly  over  his  head,  is 
not  extended  beyond  that  part  of  the  earth  which 
is  directly  under  his  body,  and  therefore  will 
not  be  visible. 

As  the  shadow  of  every  opake  body  is  extend¬ 
ed  from  the  sun,  it  follows,  that  when  the  sun 
at  noon  is  southward  from  the  zenith  of  any 
place,  the  shadow  of  an  inhabitant  of  that  place, 
and  indeed  of  any  other  opake  body,  is  extended 
towards  the  north. 

But  when  the  sun  is  northward  from  the 
zenith  of  any  place,  the  shadow  falls  towards 
the  south. 

Those  are  called  amphiscii,  that  have  both 
kinds  of  meridian  shadows. 

Those,  whose  meridian  shadows  are  always 
projected  one  way,  are  termed  heterosci'u 

PROBLEM  XXI. 

To  illustrate  the  distinction  of  ascii,  awphiscii,  bete~ 
roscii ,  and  periscii ,  by  the  globe . 

Rectify  the  globe  to  the  summer  solstice,  and 
move  the  artificial  horizon  to  the  equator,  the 
north  point  will  be  the  most  elevated  at  noon. 

Which  shews,  that  to  those  inhabitants 
who  live  at  the  equator,  the  sun  will  at  this 
season  appear  to  the  north  at  noon,  and  their 

264 


OF  THE  GLOBES. 


79 


shadow  will  therefore  be  projected  south¬ 
wards. 

But  if  you  rectify  the  globe  to  the  winter 
solstice,  the  south  point  being  then  the  upper¬ 
most  point  at  noon,  the  same  persons  will  at  noon 
have  the  sun  on  the  south  side  of  them,  and  will 
project  their  shadows  northwards. 

Thus  they  are  amphiscii,  projecting  their  shade 
both  ways ;  which  is  the  case  of  all  the  inha¬ 
bitants  within  the  tropics. 

The  artificial  horizon  remaining  as  before, 
rectify  the  globe  to  the  times  of  the  equinox, 
and  you  will  find  that  when  this  horizon  is  under 
the  strong  brass  meridian,  a  line  going  verti¬ 
cally  upwards  will  be  perpendicular  to  it,  and 
consequently  the  sun  will  be  directly  over  the 
heads  of  the  inhabitants,  and  they  will  be  ascii, 
having  no  noon  shade ;  their  shadow  is  in  the 
morning  projected  directly  westward,  in  the 
evening  directly  eastward. 

The  same  thing  will  also  happen  to  all  the 
inhabitants  who  live  between  the  tropics  of 
Cancer  and  Capricorn  ;  so  that  they  are  not  only 
ascii,  but  amphiscii  also. 

Those  who  live  without  the  tropics  are 
heteroscii  *,  those  in  north  latitude  have  the  noon 
shade  always  directed  to  the  north,  while  those 
in  south  latitude  have  it  always  projected  to  the 
south. 

The  inhabitants  of  the  polar  circles  are 

265 


80 


description  and  use 


called  periscii ;  because,  as  the  sun  goes  round 
them  continually,  their  shade  goes  round  them 
likewise. 

OF  ANCIENT  DISTINCTIONS  FROM  SITUATION-. 

These  terms  being  often  mentioned  by  ancient 
geographical  writers  to  express  the  different 
situation  of  parts  of  the  globe,  by  the  relation 
which  the  several  inhabitants  bore  to  one 
another,  it  will  be  necessary  to  take  some  notice 
of  them. 

The  antxci  are  two  nations  which  are  in  or 
near  the  same  meridian  ;  the  one  in  north,  the 
other  in  south  latitude. 

They  have  therefore  the  same  longitude,  but 
not  the  same  latitude ;  opposite  seasons  of  the 
year,  but  the  same  hour  of  the  day ;  the  days  of 
the  one  are  equal  to  the  nights  of  the  other,  and, 
i vice  versa ,  when  the  days  of  the  one  are  at  the 
longest,  they  are  shortest  at  the  other. 

When  they  look  towards  each  other,  the  sun 
seems  to  rise  on  the  right  hand  of  the  one,  but 
on  the  left  of  the  other.  They  have  different 
poles  elevated ;  and  the  stars  that  never  set  to 
the  one,  are  never  seen  by  the  other. 

Fenced  are  also  two  opposite  nations,  situated 
on  the  same  parallel  of  latitude. 

They  have  therefore  the  same  latitude,  but 
differ  1 80  degrees  in  longitude  $  the  same  sea- 

266 


OF  THE  GLOBES. 


81 


sons  of  the  year,  but  opposite  hours  of  the  day  ; 
for  when  it  is  twelve  at  night  to  the  one,  it  is 
twelve  at  noon  with  the  other.  On  the  equi¬ 
noctial  days,  the  sun  is  rising  to  one,  when  it  is 
setting  to  the  other. 

Antipodes  are  two  nations  diametrically,  oppo¬ 
site,  which  have  opposite  seasons  and  latitude, 
opposite  hours  and  longitude. 

The  sun  and  stars  rise  to  the  one,  when  they 
set  to  the  other,  and  that  during  the  whole  year, 
for  they  have  the  same  horizon. 

The  day  of  the  one  is  the  night  of  the  other; 
and  when  the  day  is  longest  with  the  one,  the 
other  has  it’s  shortest  day. 

They  have  the  contrary  seasons  at  the  same 
time  ;  different  poles,  but  equally  elevated  ;  and 
those  stars  that  are  always  above  the  horizon  of 
one,  are  always  under  the  horizon  of  the  other, 

PROBLEM  XXII. 

To  find  the  Antceci ,  the  Periceci ,  and  the  Antipodes 

of  any  place . 

Bring  the  given  place  to  the  strong  brass  me¬ 
ridian,  then  in  the  opposite  hemisphere,  and  un¬ 
der  the  same  degree  of  latitude  with  the  given 
place,  you  will  find  the  antoeci. 

The  given  place  remaining  under  the  me¬ 
ridian,  set  the  horary  index  to  XII ;  then  turn 

L  267 


82 


description  and  use 


the  globe,  till  the  other  XII  is  under  the  index, 
then  will  you  find  the  perioeci  under  the  same 
degree  of  latitude  with  the  given  place. 

Thus  the  inhabitants  of  the  south  part  of 
Chili  are  antoeci  to  the  people  of  New  England, 
w7hose  Perioeci  are  those  Tartars  who  dwell  on 
the  north  borders  of  China,  which  Tartars 
have  the  said  inhabitants  of  Chili  for  their  anti- 

This  will  become  evident,  by  placing  the 
globe  in  the  position  of  a  right  sphere,  and 
bringing  those  nations  to  the  edge  of  the  broad 
paper  circle. 

PROBLEM  XXIII. 

The  day  of  the  month  being  given ,  to  find  all  those 
places  on  the  globe ,  over  whose  zenith  the  sun 
will  pass  on  that  day . 

Rectify  the  terrestrial  globe,  by  bringing  the 
given  day  of  the  month  on  the  back  side  of  the 
strong  brass  meridian,  to  coincide  with  the  plane 
of  the  broad  paper  circle ;  observe  the  number 
of  degrees  of  the  brass  meridian,  which  corres¬ 
ponds  to  the  given  day  of  the  month. 

This  number  of  degrees,  counted  from  the 
equator  on  the  strong  brass  meridian,  towards 
the  elevated  pole,  is  the  point  over  which  the 
sun  is  vertical ;  and  all  those  places,  which  pass 

268 


OF  THE  GLOBES. 


83 


under  this  point,  have  the  sun  directly  vertical 
on  the  given  day. 

Example*  Bring  the  1 1th  of  May  to  coincide 
with  the  plane  of  the  broad  paper  circle,  and  the 
said  plane  will  cut  eighteen  degrees  for  the  eleva¬ 
tion  of  the  pole,  which  is  equal  to  the  sun’s  de¬ 
clination  for  that  day,  which  being  counted  on 
the  strong  brass  meridian  towards  the  elevated 
pole,  is  the  point  over  which  the  sun  will  be 
vertical ;  and  all  places  that  are  under  this  de¬ 
gree,  will  have  the  sun  on  their  zenith  on  the 
1 1th  of  May. 

Hence,  when  the  sun’s  declination  is  equal  to 
the  latitude  of  any  place  in  the  torrid  zone,  the 
sun  will  be  vertical  to  those  inhabitants  that  day ; 
which  furnishes  us  with  another  method  of  solv¬ 
ing  this  problem* 

OF  PROBLEMS  PECULIAR  TO  THE  SUN. 

PROBLEM  XXIV. 

To  find  the  sun9  s  place  on  the  broad  paper  circle . 

Consider  whether  the  year  in  which  you  seek 
the  sun’s  place  is  bissextile,  or  whether  it  is  the 
first,  second,  or  third  year  after. 

If  it  be  the  first  year  after  bissextile,  those 
divisions  to  which  the  numbers  for  the  days  of 
the  months  are  affixed,  are  the  divisions  which 

269 


i 


84 


description  and  use 


are  to  be  taken  for  the  respective  days  of  each 
month  of  that  year  at  noon  ;  opposite  to  which, 
in  the  circle  of  twelve  signs,  is  the  sun’s  place. 

If  it  be  the  second  year  after  bissextile,  the 
first  quarter  of  a  day  backwards,  or  towards  the 
left  hand,  is  the  day  of  the  month  for  that  year, 
against  which,  as  before,  is  the  sun’s  place. 

If  it  be  the  third  year  after  bissextile,  then 
three  quarters  of  a  day  backwards  is  the  day  of 
the  month  lor  that  year,  opposite  to  which  is 
the  sun’s  place. 

If  the  year  in  which  you  seek  the  sun’s  place 
be  bissextile,  then  three  quarters  of  a  day  back¬ 
wards  is  the  day  of  the  month  from  the  1st  of 
January  to  the  28th  of  February  inclusive.  The 
intercalary,  or  29th  day,  is  three-fourths  of  a  day 
to  the  left  hand  from  the  1st  of  March,  and  the 
1st  of  March  itself  one  quarter  of  a  day  forward, 
from  the  division  marked  1  ;  and  so  for  every 
day  in  the  remaining  part  of  the  leap  year ;  and 
opposite  to  these  divisions  is  the  sun’s  place. 

In  this  manner  the  intercalary  day  is  very  well 
introduced  every  fourth  year  into  the  calendar, 
and  the  sun’s  place  very  nearly  obtained,  accord¬ 
ing  to  the  Julian  reckoning. 

270 


OF  THE 

GLOBES. 

85 

Thus, 

- 

A.  D 

Sun’s  place. 

Apr. 

9  ^ 

1788  Bissextile 

8 

5° 

35 

1789  First  year  after 

8 

5 

21 

1790  Second 

8 

5 

6 

1791  Third 

-  -  S 

4 

55 

Upon  my  father’s  globes  there  are  twenty- 
three  parallels,  drawn  at  the  distance  of  one 
degree  from  each  other  on  both  sides  the  equa¬ 
tor,  which,  with  two  other  parallels  at  23  2  de¬ 
grees  distance,  include  the  ecliptic  circle. 

The  two  outermost  circles  are  called  the  tro¬ 
pics  ;  that  on  the  north  side  the  equator  is  called 
the  tropic  of  Cancer,  that  which  is  on  the  south 
side,  the  tropic  of  Capricorn. 

Now  as  the  ecliptic  is  inclined  to  the  equator,  in 
an  angle  of  23]  degrees,  and  is  included  between 
the  tropics,  every  parallel  between  these  must 
cross  the  ecliptic  in  two  points,  which  two  points 
shew  the  sun’s  place  when  he  is  vertical  to  the 
inhabitants  of  that  parallel  ;  and  the  days  of  the 
month  upon  the  broad  paper  circle  answering 
to  those  points  of  the  ecliptic,  are  the  days  on 
which  the  sun  passes  directly  over  their  heads  at 
noon,  and  which  are  sometimes  called  their  two 
midsummer  days. 

It  is  usual  to  call  the  sun’s  diurnal  paths 
parallels  to  the  equator,  which  are  therefore 
aptly  represented  by  the  above-mentioned  pa- 

27) 


86 


DESCRIPTION  AND  USE 


rallel  circle;  though  his  path  is  properly  a 
spiral  line,  which  he  is  continually  describing 
all  the  year  appearing  to  move  daily  about  a 
degree  in  the  ecliptic. 

PROBLEM  XXV. 

To  find  the  sun’s  declination ,  and  thence  the  paral¬ 
lel  of  latitude  corresponding  thereto . 

Find  the  sun’s  place  for  the  given  day  in 
the  broad  paper  circle,  by  the  preceeding  prob¬ 
lem,  and  seek  that  place  in  the  ecliptic  line  upon 
the  globe  ;  this  will  shew  the  parallel  of  the 
sun’s  declination  among  the  above-mentioned 
dotted  lines,  which  is  also  the  corresponding 
parallel  of  latitude  ;  therefore  all  those  places, 
through  which  this  parallel  passes,  have  the  sun 
in  their  zenith  at  noon  on  the  given  day. 

Thus  on  the  23d  of  May  the  sun’s  declination 
will  be  about  20  deg.  10  min. ;  and  upon  the 
23d  of  August  it  will  be  1 1  deg.  13  min.  What 
has  been  said  in  the  first  part  of  this  problem, 
will  lead  the  reader  to  the  solution  of  the  fol¬ 
lowing. 


272 


OF  THE  GLOBES. 


87 


PROBLEM  XXVI. 

To  find  the  two  days  on  which  the  sun  is  in  the  ze¬ 
nith  of  any  given  place  that  is  situated  between 
the  two  tropics . 

That  parallel  of  declination,  which  passes 
through  the  given  place,  will  cut  the  ecliptic  line 
upon  the  globe  in  two  points,  which  denote  the 
sun’s  place,  against  which,  on  the  broad  paper 
circle,  are  the  days  and  months  required.  Thus 
the  sun  is  vertical  at  Barbadoes  April  24,  and 
August  18. 


PROBLEM  XXVII. 

r 

The  day  and  hour  at  any  place  in  the  torrid  zone 
being  given ,  to  find  where  the  sun  is  vertical  at 
that  Ume . 

Rectify  the  globe  to  the  day  of  the  month, 
and  you  have  the  sun’s  declination ;  bring  the 
given  place  to  the  meridian,  and  set  the  hour  in¬ 
dex  to  XII;  turn  the  globe  till  the  index  points 
to  the  given  hour  on  the  equator ;  then  will  the 
place  be'  under  the  degree  of  the  declination 
previously  found. 

Let  the  given  place  be  London,  and  time 
the  1 1  th  day  of  May,  at  4  min.  past  V  in  the 
afternoon  ;  bring  the  11th  of  May  to  coincide 
with  the  broad  paper  circle,  and  opposite  to  it 

273 


88 


DESCRIPTION  AND  USE 


\ 


you  will  find  18  degrees  of  north  declination  £ 
as  London  is  the  given  place,  you  have  only  to 
turn  the  globe  till  4  min.  past  V  westward  of  it 
is  on  the  meridian,  when  you  will  find  Port- 
Royal,  in  Jamaica,  under  the  18th  degree  of  the 
meridian,  which  is  the  place  where  the  sun  is 
vertical  at  that  time. 

PROBLEM  XXVIII. 

The  time  of  the  day  at  any  one  place  being  given  f 
to  find  all  those  places  where  at  the  same  instant 
the  sun  is  rising, ,  setting ,  and  on  the  meridian , 
and  where  he  is  vertical ;  likewise  those  places 
where  it  is  midnight ,  twilight ,  and  dark  night ; 
as  well  as  those  places  in  which  the  twilight  U 
beginning  and  ending  ;  and  also  to  find  the  sun’sr 
altitude  at  any  hour  in  the  illuminated ,  and  his 
depression  in  the  obscure ,  hemisphere . 

Rectify  the  globe  to  the  day  of  the  month,'  on 
the  back  side  of  the  strong  brass  meridian,  and 
the  sun’s  declination  for  that  day;  bring  the 
given  place  to  the  strong  brass  meridian,  and  set 
the  horary  index  to  XII  upon  the  equator ;  turn 
the  globe  from  west  to  east,  until  the  horary  in¬ 
dex  points  to  the  given  time.  Then 

All  those  places,  which  lie  in  the  plane  of 
the  western  side  of  the  broad  paper  circle,  see 

274 


OF  THE  GLOBES. 


89 


the  sun  rising,  and  at  the  same  time  those  on 
the  eastern  side  of  it  see  him  setting. 

It  is  noon  to  all  the  inhabitants  of  those  places 
under  the  upper  half  of  the  graduated  side  of 
the  strong  brass  meridian,  whilst  at  the  same 
time  those  under  the  lower  half  have  mid-night. 

All  those  places  which  are  between  the  upper 
surface  of  the  broad  paper  circle,  and  the  wire 
circle  under  it,  are  in  the  twilight,  which  begins 
to  all  those  places  on  the  western  side  that  are 
immediately  under  the  wire  circle ;  it  ends  at  all 
those  which  are  in  the  plane  of  the  paper  circle. 

The  contrary  happens  on  the  eastern  side  \ 
the  twilight  is  just  beginning  to  those  places  in 
which  the  sun  is  setting,  and  it’s  end  is  at  the 
place  just  under  the  wire  circle. 

And  those  places  which  are  under  the  twi¬ 
light  wire  circle  have  dark  night,  unless  the 
moon  is  favourable  to  them. 

All  places  in  the  illuminated  hemisphere  have 
the  sun’s  latitude  equal  to  their  distance  from 
the  edge  of  the  enlightened  disk,  which  is  known 
by  fixing  the  quadrant  of  altitude  to  the  zenith, 
and  laying  it’s  graduated  edge  over  any  parti¬ 
cular  place. 

The  sun’s  depression  is  obtained  in  the  same 
manner,  by  fixing  the  center  of  the  quadrant  at 
the  nadir. 


M  275 


DESCRIPTION  and  use 


PROBLEM  XXIX. 

To  find  all  those  places  within  the  polar  circles  on 
which  the  sun  begins  to  shine ,  the  time  he  shines 
constantly ,  when  he  begins  to  disappear ,  the 
length  of  his  absence ,  as  well  as  the  first  and 
last  day  of  his  appearance  to  those  inhabitants  ; 
the  day  of  the  month ,  or  latitude  of  the  place 
being  given. 

Bring  the  given  day  of  the  month  on  the 
back  side  of  the  strong  brass  meridian  to  the 
plane  of  the  broad  paper  circle  ;  the  sun  is  just 
then  beginning  to  shine  on  all  those  places 
which  are  in  the  parallel  that  just  touches  the 
edge  of  the  broad  paper  circle,  and  will  for 
several  days  seem  to  skim  all  around,  and  but 
a  little  above  their  horizon,  just  as  it  appears  to 
us  at  it’s  setting ;  but  with  this  observable  dif¬ 
ference,  that  whereas  our  setting  sun  appears 
in  one  part  of  the  horizon  only,  by  them  it  is 
seen  in  every  part  thereof;  from  west  to  south, 
thence  east  to  north,  and  so  to  west  again. 

Or  if  the  latitude  be  given,  elevate  the  globe 
to  that  latitude,  and  on  the  back  of  the  strong 
brass  meridian,  opposite  to  the  latitude,  you  ob¬ 
tain  the  day  of  the  month  ;  then  all  the  other 
requisites  are  answered  as  above. 

As  the  two  concentric  spaces,  which  con- 
rain  the  days  of  the  month  on  the  back  side  of 

276 


OF  THE  GLOBES® 


the  strong  brass  meridian,  are  graduated  to  shew 
the  opposite  days  of  the  year,  at  1 80  degrees  dis¬ 
tance  ;  when  the  given  day  is  brought  to  coin¬ 
cide  with  the  broad  paper  circle,  it  shews  when 
the  sun  begins  to  shine  on  that  parallel,  which  is 
the  first  day  of  it’s  appearance  above  the  horizon 
of  that  parallel. 

And  the  plane  of  the  broad  paper  circle  cuts 
the  day  of  the  month  on  the  opposite  concentric 
space,  when  the  sun  begins  to  disappear  to  those 
inhabitants. 

The  length  of  the  longest  day  is  obtained  by 
reckoning  the  number  of  days  between  the  two 
opposite  days  found  as  above,  and  their  differ¬ 
ence  from  365  gives  the  length  of  the  longest 
night. 


PROBLEM  XXX. 


To  make  use  of  the  globe  as  a  tellurian,  or  that 
kind  of  orrery  which  is  chief  y  intended  to  illus-. 
irate  the  phenomena  that  arise  from  the  annual 
and  diurnal  motions  of  the  earth . 


i  . 

Describe  a  circle  with  chalk  upon  the  floor, 
as  large  as  the  room  will  admit  of,  so  that  the 
globe  may  be  moved  round  upon  it ;  divide  this 
circle  into  twelve  parts,  and  mark  them  with 
the  characters  of  the  twelve  signs,  as  they  are 
engraved  upon  the  broad  paper  circle ;  pla¬ 
cing  25  at  the  north,  vj  at  the  south,  ^  ir> 

277 


25 


92 


DESCRIPTION  AND  USE 


the  east,  and  =£=  in  the  west :  the  mariner’s  com¬ 
pass  under  the  globe  will  direct  the  situation  of 
these  points,  if  the  variation  of  the  magnetic 
needle  be  attended  to. 

Note,  At  London  the  variation  is  between  23 
and  24  degrees  from  the  north-westward. 

Elevate  the  north  pole  of  the  globe,  so  that 
66 *  degrees  on  the  strong  brass  meridian  may 
coincide  with  the  surface  of  the  broad  paper 
circle,  and  this  circle  will  then  represent  the 
plane  of  the  ecliptic,  or  a  plane  coinciding  with 
the  earth’s  orbit. 

Set  a  small  table,  or  a  stool,  over  the  center 
of  the  chalked  circle,  to  represent  the  sun,  and 
place  the  terrestrial  globe  upon  it’s  circum¬ 
ference  over  the  point  marked  ,  with  the  north 
pole  facing  the  imaginary  sun,  and  the  north 
end  of  the  needle  pointing  to  the  variation ; 
and  the  globe  will  be  in  the  position  of  the 
earth  with  respect  to  the  sun  at  the  time  of  the 
summer  solstice,  about  the  21st  of  June;  and 
the  earth’s  axis,  by  this  rectification  of  the  globe, 
is  inclined  to  the  plane  of  the  large  chalked 
circle,  as  well  as  to  the  plane  of  the  broad 
paper  circle,  in  an  angle  of  66]  degrees;  a 
line,  or  string,  passing  from  the  center  of 
the  imaginary  sun  to  that  of  the  globe,  will 
represent  a  central  solar  ray  connecting  the 
centers  of  the  earth  and  sun  :  this  ray  will  fall 
upon  the  first  point  of  Cancer,  and  describe 

O* 7« 


©F  THE  GLOBES. 


93 

that  circle,  shewing  it  to  be  the  sun’s  place 
upon  the  terrestrial  ecliptic,  which  is  the  same 
as  if  the  sun’s  place,  by  extending  the  string, 
was  referred  to  the  opposite  side  of  the  chalked 
circle,  here  representing  the  earth’s  path  in  the 
heavens. 

If  we  conceive  a  plane  to  pass  through  the 
center  of  the  globe  and  the  sun’s  center,  it  will 
also  pass  through  the  points  of  Cancer  and  Ca¬ 
pricorn,  in  the  terrestrial  and  celestial  ecliptic ; 
the  central  solar  ray,  in  this  position  of  the  earth, 
is  also  in  that  plane  :  this  can  never  happen  but 
at  the  times  of  the  solstice. 

If  another  plane  be  conceived  to  pass  through 
the  center  of  the  globe  at  right  angles  to  the 
center  solar  ray,  it  will  divide  the  globe  into  two 
hemispheres  ;  that  next  the  center  of  the  chalked 
circle  will  represent  the  earth’s  illuminated  disk, 
the  contrary  side  of  the  same  plane  will  at  the 
same  time  shew  the  obscure  hemisphere. 

The  reader  may  realize  this  second  plane  by 
cutting  away  a  semicircle  from  a  sheet  of  card 
paste  board,  with  a  radius  of  about  1|  tenth  of 
an  inch  greater  than  that  of  the  globe  itself.* 

If  this  plane  be  applied  to  66J  degrees  upon 
the  strong  brass  meridian,  it  will  be  in  the 
pole  of  the  ecliptic  ;  and  in  every  situation  of 


*  Or  he  may  have  a  plane  made  of  wood  for  this  purpose, 

279 


94 


DESCRIPTION  AND  USE 


the  globe  round  the  circumference  of  the  chalk¬ 
ed  circle,  it  will  afford  a  lively  and  lasting  idea 
of  the  various  phenomena  arising  from  the  par¬ 
allelism  of  the  earth’s  axis,  and  in  particular  the 
daily  change  of  the  sun’s  declination,  and  the 
parallels  thereby  described. 

Let  the  globe  be  removed  from  to  xz, 
and  the  needle  pointing  to  the  variation  as  be¬ 
fore,  will  preserve  the  parallelism  of  the  earth’s 
axis ;  then  it  will  be  plain  that  the  string,  or 
central  solar  ray,  will  fail  upon  the  first  point  of 
Leo,  six  signs  distant  from,  but  opposite  to  the 
sign  upon  which  the  globe  stands ;  the  cen¬ 
tral  solar  ray  will  now  describe  the  20th  par¬ 
allel  of  north  declination,  which  will  be  about 
the  25d  of  July. 

If  the  globe  be  moved  in  this  manner  from 
point  to  point  round  the  circumference  of  the 
chalked  circle,  and  care  be  taken  at  every  re¬ 
moval  that  the  north  end  of  the  magnetic  needle, 
when  settled,  points  to  the  degree  of  variation, 
the  north  pole  of  the  globe  will  be  observed  to 
recede  from  the  line  connecting  the  centers  of 
the  earth  and  sun,  until  the  globe  is  placed  upon 
the  point  Cancer ;  after  which,  it  will  at  every 
removal  tend  more  and  more  towards  the  said 
line,  till  it  comes  to  Capricorn  again. 

280 


OF  THE  GLOBES. 


95 


PROBLEM.  XXXI. 

To  rectify  either  globe  to  the  latitude  and  horizon 

of  any  place. 

If  the  place  be  in  north  latitude,  raise  the 
north  pole ;  if  in  south  latitude,  raise  the  south 
pole,  until  the  degree  of  the  given  latitude, 
reckoned  on  the  strong  brass  meridian  under 
the  elevated  pole,  cuts  the  plane  of  the  broad 
paper  circle ;  then  this  circle  will  represent  the 
horizon  of  that  place,  while  the  place  remains  in 
the  zenith,  but  no  longer.  This  rectification  is 
therefore  unnatural,  though  it  is  the  mode  adopt¬ 
ed  in  using  the  globes  when  mounted  in  the 
old  manner. 

PROBLEM  XXXII. 

To  rectify  for  the  sun’s  place. 

After  the  former  rectification,  bring  the 
degrees  of  the  sun’s  place  in  the  ecliptic  line 
upon  the  globe  to  the  strong  brass  meridian, 
and  set  the  horary  index  to  that  Xllth  hour 
upon  the  equator  which  is  most  elevated. 

Or  if  the  sun’s  place  is  to  be  retained,  to 
answer  various  conclusions,  bring  the  gra¬ 
duated  edge  of  the  moveable  meridian  to  the 
degree  of  the  sun’s  place  in  the  ecliptic,  and 
slide  the  wire  which  crosses  the  center  of  the 


283 


96 


DESCRIPTION  AND  USE 


artificial  horizon  thereto;  then  bring  it’s  center, 
which  is  in  the  intersection  of  the  aforesaid  wire, 
and  graduated  edge  of  the  moveable  meridian, 
under  the  srrong  brass  meridian  as  before,  and 
set  the  horary  index  to  that  XII  on  the  equator 
which  is  most  elevated. 


PROBLEM  XXXIII. 


To  rectify  for  the  zenith  of  any  place. 

After  the  first  rectification,  screw  the  nut  of 
the  quadrant  of  altitude  so  many  degrees  from 
the  equator,  reckoned  on  the  strong  brass  meri¬ 
dian  towards  the  elevated  pole,  as  that  pole  is 
raised  above  the  plane  of  the  broad  paper  circle, 
and  that  point  will  represent  the  zenith  of  the 
place. 

Note ,  The  zenith  and  nadir  are  the  poles  of 
the  horizon,  the  former  being  a  point  directly 
over  our  heads,  and  the  latter,  one  directly 
under  our  feet. 

If,  when  the  globe  is  in  this  state,  we  look  on 
the  opposite  side,  the  plane  of  the  horizon  will 
cut  the  strong  brass  meridian  at  the  comple¬ 
ment  of  the  latitude,  which  is  also  the  elevation 
of  the  equator  above  the  horizon. 


OF  THE  GLOBES. 


97 


OF  THE  SOLUTION  OF  PROBLEMS,  BY  EXPOS¬ 
ING  THE  GLOBES  TO  THE  SUN’S  RAYS. 

In  the  year  1679,  J.  Moxon  published  a  trea¬ 
tise  on  what  he  called  “  The  English  Globe  ;  be¬ 
ing  (says  he)  a  stabil  and  immobil  one,  perform¬ 
ing  what  the  ordinary  globes  do,  and  much 
more  ;  invented  and  described  by  the  Right 
Hon.  the  Earle  of  Castlemaine .”  This  globe  was 
designed  to  perform,  by  being  merely  exposed 
to  the  sun’s  rays,  all  those  problems  which  in 
the  usual  way  are  solved  by  the  adventitious  aid 
of  brazen  meridians,  hour  indexes,  &c. 

My  father  thought  that  this  method  might 
be  useful,  to  ground  more  deeply  in  the  young 
pupil’s  mind,  those  principles  which  the  globes 
are  intended  to  explain  ;  and  by  giving  him  a 
different  view  of  the  subject,  improve  and 
strengthen  his  mind  ;  he  therefore  inserted  on 
his  globes  some  lines,  for  the  purpose  of  solv¬ 
ing  a  few  problems  in  Lord  Castlemaine’s  man¬ 
ner. 

It  appears  to  me,  from  a  copy  of  Moxon’s 
publication,  which  is  in  my  possession,  that  the 
Earle  of  Castlemaine  projected  a  new  edition  of 
his  works,  as  the  copy  contains  a  great  number 
of  corrections,  many  alterations,  and  some  ad¬ 
ditions.  It  is  not  very  improbable,  that  at  some 

N  283 


98  description  and  use 

future  day  I  may  re-publish  this  curious  Work, 
and  adapt  a  small  globe  for  the  solution  of  the 
problems. 

The  meridians  on  our  new  terrestrial  globes 
being  secondaries  to  the  equator,  are  also  hour 
circles,  and  are  marked  as  such  with  Roman 
figures,  under  the  equator,  and  at  the  polar  cir¬ 
cles.  Rut  there  is  a  difference  in  the  figures 
placed  to  the  same  hour  circle ;  if  it  cuts  the 
Hid  hour  upon  the  polar  circles,  it  will  cut  the 
IX  hour  upon  the  equator,  which  is  six  hours 
later,  and  so  of  all  the  rest. 

Through  the  great  Pacific  sea,  and  the  inter¬ 
section  of  Libra,  is  drawn  a  broad  meridian  from 
pole  to  pole ;  it  passes  through  the  Xllth  hour 
upon  the  equator,  and  the  Vlth  hour  upon  each 
of  the  polar  circles  ;  this  hour  circle  is  graduated 
into  degrees  and  parts,  and  numbered  from  the 
equator  towards  either  pole. 

There  is  another  broad  meridian  passing 
through  the  Pacific  sea,  at  the  IX th  hour  upon 
the  equator,  and  the  Illd  hour  upon  each  polar 
circle  ;  this  contains  only  one  quadrant,  or  90 
degrees  ;  the  numbers  annexed  to  it  begin  at  the 
northern  polar  circle,  and  end  at  the  tropic  of 
Capricorn. 

Here  we  must  likewise  observe,  there  are  23 
concentric  circles  drawn  upon  the  terrestrial 
globe  within  the  northern  and  southern  polar 
circles,  which  for  the  future  we  shall  call  pofar 

284 


OF  THE  GLOBES. 


99 


parallels  ;  they  are  placed  at  the  distance  of  one 
degree  from  each  other,  and  represent  the  pa¬ 
rallels  of  the  sun’s  declination,  but  in  a  differ¬ 
ent  manner  from  the  47  parallels  between  the 
tropics. 

The  following  problems  require  the  globe  to 
be  placed  upon  a  plane  that  is  level,  or  truly 
horizontal,  which  is  easily  attained,  if  the  floor, 
pavement,  gravel-walk  in  the  garden,  &c.  should 
not  happen  to  be  horizontal. 

A  flat  seasoned-  board,  or  any  box  which  is 
about  two  feet  broad,  or  two  feet  square,  if  the 
top  be  perfectly  flat,  will  answer  the  purpose ; 
the  upper  surface  of  either  may  be  set  truly 
horizontal,  by  the  help  of  a  pocket  spirit  level, 
or  plumb  rule,  if  you  raise  or  depress  this  or 
that  side  by  a  wedge  or  two,  as  the  spirit  level 
shall  direct :  if  vou  have  a  meridian  line  drawn 
on  the  place  over  which  you  substitute  this  ho¬ 
rizontal  plane,  it  may  be  readily  transferred  from 
thence  to  the  surface  just  levelled  ;  this  being 
done,  we  are  prepared  for  the  solution  of  the 
following  problems. 

It  will  be  necessary  to  define  a  term  we  are 
obliged  to  make  use  of  in  the  solution  of  these 
problems,  namely,  the  shade  of  extuberancy  :  by 
this  is  meant  that  shade  which  is  caused  by  the 
sphericity  cf  the  globe,  and  answers  to  what 
we  have  heretofore  named  the  terminator,  de¬ 
fining  the  boundaries  of  the  illuminated  and 

‘185 


100 


DESCRIPTION  AND  USE 


« 

obscure  parts  of  the  globe ;  this  circle  was,  in 
the  solution  of  some  of  the  foregoing  problems, 
represented  by  the  broad  paper  circle,  but  is  here 
realized  by  the  rays  of  the  sun. 

PROBLEM  XXXIV. 

To  observe  the  sun’s  altitude  (by  the  terrestrial 
globe )  when  he  shines  bright ,  or  when  he  can 
but  just  be  discerned  through  a  cloud. 

Elevate  the  north  pole  of  the  globe  to  661- 
degrees  ;  bring  that  meridian,  or  hour  circle, 
which  passes  through  the  IXth  hour  upon  the 
equator,  under  the  graduated  side  of  the  strong 
brass  meridian ;  the  globe  being  now  set  upon 
the  horizontal  plane,  turn  it  about  thereon, 
frame  and  all,  that  the  shadow  of  the  strong 
brass  meridian  may  fall  directly  under  itself ; 
or  in  other  words,  that  the  shade  of  it’s  gra¬ 
duated  face  may  fall  exactly  upon  the  aforesaid 
hour  circle ;  at  that  instant  the  shade  of  extu- 
berancy  will  touch  the  true  degree  of  the  sun’s 
altitude  upon  that  meridian,  which  passes 
through  the  IXth  hour  upon  the  equator,  reck¬ 
oned  from  the  polar  circle,  the  most  elevated 
part  of  which  will  then  be  in  the  zenith  of  the 
place  where  this  operation  is  performed,  and 
is  the  same  whether  it  should  happen  to  be 
either  in  north  or  south  latitude. 

Thus  we  may,  in  an  easy  and  natural  man- 

286 


OF  THE  GLOBES. 


101 


ner,  obtain  the  altitude  of  the  sun,  at  any  time 
of  the  day,  by  the  terrestrial  globe  ;  for  it  is  very 
plain,  when  the  sun  rises,  he  brushes  the  zenith 
and  nadir  of  the  globe  by  his  rays ;  and  as  he 
’always  illuminates  half  of  it,  (or  a  few  minutes 
more,  as  his  globe  is  considerably  larger  than 
that  of  the  earth)  therefore  when  the  sun  is  risen 
a  degree  higher,  he  must  necessarily  illuminate 
a  degree  beyond  the  zenith,  and  so  on  propor- 
tionably  from  time  to  time. 

But  as  the  illuminated  part  is  somewhat  more 
than  half,  deduct  13  minutes  from  the  shade 
of  extuberancy,  and  you  have  the  sun’s  altitude 
with  tolerable  exactness. 

If  you  have  any  doubt  how  far  the  shade  of 
extuberancy  reaches,  hold  a  pin,  or  your  finger, 
on  the  globe,  between  the  sun  and  point  in  dis¬ 
pute,  and  where  the  shade  of  either  is  lost,  will 
be  the  point  sought. 

v 

When  the  sun  does  not  shine  bright  enough  to  cast  a 

shadow. 

Turn  the  meridian  of  the  globe  towards  the 
sun,  as  before,  or  direct  it  so  that  it  may  lie  in 
the  same  plane  with  it,  which  may  be  done  if 
you  have  but  the  least  glimpse  of  the  sun 
through  a  cloud  ;  hold  a  string  in  both  hands, 
it  having  first  been  put  between  the  strong 
brass  meridian  and  the  globe ;  stretch  it  at 

287 


102 


DESCRIPTION  AND  USE 


right  angles  to  the  meridian,  and  apply  your 
face  near  to  the  globe,  moving  your  eye  lower 
and  lower,  till  you  can  but  just  see  the  sun  ;  then 
bring  the  string  held  as  before  to  this  point 
upon  the  globe,  that  it  may  just  obscure  the 
sun  from  your  sight,  and  the  degree  on  the 
aforesaid  hour  circle,  which  the  string  then  lies 
upon,  will  be  the  sun’s  altitude  required,  for  his 
rays  would  shew  the  same  point  if  he  shone  out 
bright. 

Note.  The  moon’s  altitude  may  be  observed 
by  either  of  these  methods,  and  the  altitude  of 
any  star  by  the  last  of  them. 


PROBLEM  XXXV. 

To  place  the  terrestrial  globe  in  the  sunys  rays ,  that 
it  may  represent  the  natural  position  of  the  earthy 
cither  by  a  meridian  line ,  or  without  it. 

If  you  have  a  meridian  line,  set  the  north 
and  south  points  of  the  broad  paper  circle  di¬ 
rectly  over  it,  the  north  pole  of  the  globe  being 
elevated  to  the  latitude  of  the  place,  and  stand¬ 
ing  upon  a  level  plane,  bring  the  place  you  are 
in  under  the  graduated  side  of  the  strong  brass 
meridian,  then  the  poles  and  parallel  circles 
upon  the  globe  will,  without  sensible  error, 
correspond  with  those  in  the  heavens,  and  each 

288 


OF  THE  GLOBES,  103 

point,  kingdom,  and  state,  will  be  turned  to¬ 
wards  the  real  one  which  it  represents. 

If  you  have  no  meridian  line,  then  the  day 
of  the  month  being  known,  find  the  sun’s  decli¬ 
nation  as  before  instructed,  which  will  direct 
you  to  the  parallel  of  the  day,  amongst  the 
polar  parallels,  reckoned  from  either  pole  to¬ 
wards  the  polar  circle ;  which  you  are  to  re¬ 
member. 

Set  the  globe  upon  your  horizontal  plane  in 
the  sun-shine,  and  put  it  nearly  north  and  south 
by  the  manner’s  compass,  it  being  first  elevated 
to  the  latitude  of  the  place,  and  the  place  itself 
brought  under  the  graduated  side  of  the  strong 
brass  meridian  ;  then  move  the  frame  and  globe 
together,  till  the  shade  of  extuberancy,  or  term 
of  illumination,  just  touches  the  polar  parallel 
for  the  day,  and  the  globe  will  be  settled  as 
before ;  and  if  accurately  performed,  the  varia¬ 
tion  of  the  magnetic  needle  will  be  shewn  by  the 
degree  to  which  it  points  in  the  compass  box. 

And  here  observe,  if  the  parallel  for  the  day 
should  not  happen  to  fall  on  any  one  of  those 
drawn  upon  the  globe,  you  are  to  estimate  a, 
proportionable  part  between  them,  and  reckon 
that  the  parallel  of  the  day.  If  we  had  drawn 
more,  the  globe  would  have  been  confused. 

The  reason  of  this  operation  is,  that  as  the 

264 


104 


DESCRIPTION  AND  USE 


sun  illuminates  half  the  globe,  the  shade  of  ex¬ 
uberancy  will  constantly  be  90  degrees  from  the 
point  wherein  the  sun  is  vertical. 

If  the  sun  be  in  the  equator,  the  shade  and 
illumination  must  terminate  in  the  poles  of  the 
world ;  and  when  he  is  in  any  other  diurnal 
parallel,  the  terms  of  illumination  must  fall 
short  of,  or  go  beyond  either  pole,  as  many  de¬ 
grees  as  the  parallel  which  the  sun  describes  that 
day  is  distant  from  the  equator  ;  therefore,  when 
the  shade  of  extuberancy  touches  the  polar  par¬ 
allel  for  the  day,  the  artificial  globe  will  be  in 
the  same  position,  with  respect  to  the  sun,  as  the 
earth  really  is,  and  will  be  illuminated  in  the 
same  manner. 

PROBLEM  XXXVI. 

To  find  naturally  the  sun’s  decimation ,  diurnal 
■parallel ,  and  his  place  thereon . 

The  globe  being  set  upon  an  horizontal 
plane,  and  adjusted  by  a  meridian  line  or  other¬ 
wise,  observe  upon  which,  or  between  which 
polar  parallel  the  term  of  illumination  falls  ;  it’s 
distance  from  the  pole  is  the  degree  of  the  sun’s 
declination ;  reckon  this  distance  from  the 
equator  among  the  larger  parallels,  and  you 
have  the  parallel  which  the  sun  describes  that 
day  ;  upon  which  if  you  move  a  card,  cut  in 
the  form  of  a  double  square,  until  it’s  shadow 

290 


OF  THE  GLOBES. 


105 


falls  under  Itself,  you  will  obtain  the  very  place 
upon  that  parallel  over  which  the  sun  is  vertical 
at  any  hour  of  that  day,  if  you  set  the  place  you 
are  in  under  the  graduated  side  of  the  strong 
brass  meridian. 

Note,  The  moon’s  declination,  diurnal  paral¬ 
lel,  and  place,  may  be  found  in  the  same  manner. 
Likewise,  when  the  sun  does  not  shine  bright, 
his  declination,  &c.  may  be  found  by  an  appli¬ 
cation  in  the  manner  of  problem  xxxiv. 


PROBLEM  XXXVII. 

To  find  the  surfs  azimuth  naturally , 

If  a  great  circle,  at  right  angles  to  the  horizon, 
passes  through  the  zenith  and  nadir,  and  also 
through  the  sun’s  center,  it’s  distance  from  the 
meridian  in  the  morning  or  evening  of  any  day, 
reckoned  upon  the  degrees  on  the  inner  edge  of 
the  broad  paper  circle,  will  give  the  azimuth 
required. 

Method  1* 

Elevate  either  pole  to  the  position  of  a  pa¬ 
rallel  sphere,  by  bringing  the  north  pole  in 
north  latitude,  and  the  south  pole  in  south  lati¬ 
tude,  into  the  zenith  of  the  broad  paper  circle, 
having  first  placed  the  globe  upon  your  meri- 

O  291 


106  DESCRIPTION  AND  USE 

.  1  \ 

dian  line,  or  by  the  other  method  before  pre¬ 
scribed  ;  hold  up  a  plumb  line,  so  that  it  may 
pass  freely  near  the  outward  edge  of  the  broad 
paper  circle,  and  move  it  so  that  the  shadow  of 
the  string  may  fall  upon  the  elevated  pole ;  then 
cast  your  eye  immediately  to  it’s  shadow  on  the 
broad  paper  circle,  and  the  degree  it  there  falls 
upon  is  the  sun’s  azimuth  at  that  time,  which 
may  be  reckoned  from  either  the  south  or  north 
points  of  the  horizon. 

Method  ii. 

If  you  have  only  a  glimpse,  or  faint  sight  of 
the  sun,  the  globe  being  adjusted  as  before, 
stand  on  the  shady  side,  and  hold  the  plumb 
line  on  that  side  also,  and  move  it  till  it  cuts  the 
sun’s  center,  and  the  elevated  pole  at  the  same 
time  ;  then  cast  your  eye  towards  the  broad 
paper  circle,  and  the  degree  it  there  cuts  is  the 
sun’s  azimuth,  which  must  be  reckoned  from 
the  opposite  cardinal  point. 

PROBLEM  XXXVIII. 

To  shew  that  in  some  places  of  the  earth9 s  surface , 
the  sun  will  be  twice  in  the  same  azimuth  in 
the  morning ,  twice  in  the  same  azimuth  in  the 
afternoon  :  or  in  other  words , 

' 

When  the  declination  of  the  sun  exceeds 

{"  (  |*  ^  *  4 

the  latitude  of  any  place,  on  either  side  of  the 

292 


OF  THE  GLOBES. 


107 


equator,  the  sun  will  be  on  the  same  azimuth 
twice  in  the  morning,  and  twice  in  the  after¬ 
noon. 

Thus,  suppose  the  globe  rectified  to  the 
latitude  of  Antigua,  which  is  about  17  deg.  of 
north  latitude,  and  the  sun  to  be  in  the  begin¬ 
ning  of  Cancer,  or  to  have  the  greatest  north 
declination  ;  set  the  quadrant  of  altitude  to  the 
21st  degree  north  of  the  east  in  the  horizon, 
and  turn  the  globe  upon  it’s  axis,  the  sun’s 
center  will  be  on  that  azimuth  at  6  h.  30  min. 
and  also  at  10  h.  30  min.  in  the  morning.  At 
8  h.  30  min.  the  sun  will  be  as  it  were  station- 
ary,  with  respect  to  it’s  azimuth,  for  some 
time ;  as  it  will  appear  by  placing  the  quadrant 
of  altitude  to  the  17th  degree  north  of  the  east 
in  the  horizon.  If  the  quadrant  be  set  to  the 
same  degrees  north  of  the  west,  the  sun’s  center 
will  cross  it  twice  as  it  approaches  the  horizon 
in  the  afternoon. 

This  appearance  will  happen  more  or  less  to 
all  places  situated  in  the  torrid  zone,  whenever 
the  sun’s  declination  exceeds  their  latitude  ;  and 
from  hence  we  may  infer,  that  the  shadow  of  a 
dial,  whose  gnomon  is  erected  perpendicular  to 
an  horizontal  plane,  must  -  necessarily  go  back 
several  degrees  on  the  same  day. 

But  as  this  can  only  happen  within  the  tor¬ 
rid  zone,  and  as  Jerusalem  lies  about  8  degrees 

203 


108 


DESCRIPTION  AND  USE 


to  the  north  of  the  tropic  of  Cancer,  the  retro¬ 
cession  of  the  shadow  on  the  dial  of  Ahaz,  at 
Jerusalem,  was,  in  the  strictest  signification  of 
the  word,  miraculous. 

PROBLEM  XXXIX. 

To  observe  the  hour  of  the  day  in  the  most  natural 
maniier ,  when  the  terrestrial  globe  is  properly 
placed  in  the  sun-shine . 

There  are  many  ways  to  perform  this  opera¬ 
tion  with  respect  to  the  hour,  three  of  which 
are  here  inserted,  being  general  to  all  the  inha¬ 
bitants  of  the  earth  ;  a  fourth  is  added,  peculiar 
to  those  of  London,  which  will  answer,  without 
sensible  error,  at  any  place  not  exceeding  the 
distance  of  60  miles  from  this  capital. 

1st,  By  a  natural  style . 

Having  rectified  the  globe  as  before  directed, 
and  placed  it  upon  an  horizontal  plane  over 
your  meridian  line,  or  by  the  other  method,  hold 
a  long  pin  upon  the  illuminated  pole,  in  the 
direction  of  the  polar  axis,  and  it’s  shadow  will 
shew  the  hour  of  the  day  amongst  the  polar 
parallels. 

The  axis  of  the  globe  being  the  common 
section  of  the  hour  circles,  is  in  the  plane  of 
each  ;  and  as  we  suppose  the  globe  to  be  pro¬ 
perly  adjusted,  they  will  correspond  with  those 

294 


OF  THE  GLOBES.  109 

in  the  heavens ;  therefore  the  shade  of  a  pin, 
which  is  the  axis  continued,  must  fall  upon  the 
true  hour  circle. 

2dly ,  By  an  artificial  stile . 

Tie  a  small  string,  with  a  noose,  round  the 
elevated  pole,  stretch  it’s  other  end  beyond  the 
globe,  and  move  it  so  that  the  shadow  of  the 
string  may  fall  upon  the  depressed  axis  ;  at  that 
instant  it’s  shadow  upon  the  equator  will  give 
the  solar  hour  to  a  minute. 

But  remember,  that  either  the  autumnal  or 
vernal  equinoctial  colure  must  first  be  placed 
under  the  graduated  side  of  the  strong  brass 
meridian,  before  you  observe  the  hour,  each  of 
these  being  marked  upon  the  equator  with  the 
hour  XII. 

The  string  in  this  last  case  being  moved  into 
the  plane  of  the  sun,  corresponds  with  the  true 
hour  circle,  and  consequently  gives  the  true  hour. 

3dly,  Without  any  stile  at  all . 

Every  thing  being  rectified  as  before,  look 
where  the  shade  of  extuberancy  cuts  the  equa¬ 
tor,  the  colure  being  under  the  graduated  side 
of  the  strong  brass  meridian,  and  you  obtain  the 
hour  in  two  places  upon  the  equator,  one  of 
them  going  before,  and  the  other  following  the 

sun. 

295 


1 


.  ' 


110  description  and  use 

Note,  If  this  shade  be  dubious,  apply  a  pin,  or 
your  finger,  as  before  directed. 

The  reason  is,  that  the  shade  of  extuberancy 
being  a  great  circle,  cuts  the  equator  in  half, 
and  the  sun,  in  whatsoever  parallel  of  declina¬ 
tion  he  may  happen  to  be,  is  always  in  the  pole 
of  the  shade  ;  consequently  the  confines  of  light 
and  shade  will  shew  the  true  hour  of  the  day. 

4/Z>/y,  Peculiar  to  the  inhabitants  of  London ,  and 
any  place  within  the  distance  of  sixty  miles  from 
it. 

The  globe  being  every  way  adjusted  as  before, 
and  London  brought  under  the  graduated  side 
of  the  strong  brass  meridian,  hold  up  a  plumb- 
line,  so  that  it’s  shadow  may  fall  upon  the  zenith 
point,  (which  in  this  case  is  London  itself)  and 
the  shadow  of  the  string  will  cut  the  parallel  of 
the  day  upon  that  point  to  which  the  sun  is  then 
vertical,  and  that  hour  circle  upon  which  this 
intersection  falls,  is  the  hour  of  the  day  ;>and  as 
the  meridians  are  drawn  within  the  tropics,  at 
twenty  minutes  distance  from  each  other,  the 
point  cut  by  the  intersection  of  the  string  upon 
the  parallel  of  the  day,  being  so  near  the  equator, 
may,  by  a  glance  of  the  observer’s  eye,  be  re¬ 
ferred  thereto,  and  the  true  time  obtained  to  a 
minute. 

The  plumb-line  thus  moved  is  the  azimuth  ; 
which,  by  cutting  the  parallel  of  the  day,  gives 

296 


OF  THE  GLOBES.  Ill 

the  sun's  place,  and  consequently  the  hour  circle 
which  intersects  it. 

From  this  last  operation  results  a  corollary, 
that  gives  a  second  way  of  rectifying  the  globe 
to  the  sun’s  rays. 

If  the  azimuth  and  shade  of  the  illuminated 
axis  agree  in  the  hour  when  the  globe  is  recti¬ 
fied,  then  making  them  thus  to  agree,  must 
rectify  the  globe. 

COROLLARY. 

Another  method  to  rectify  the  globe  to  the  sun's 

rays . 

Move  the  globe,  till  the  shadow  of  the  plumb- 
line,  which  passes  through  the  zenith  cuts  the 
same  hour  on  the  parallel  of  the  day,  that  the 
shade  of  the  pin,  held  in  the  direction  of  the 
axis,  falls  upon,  amongst  the  polar  parallels,  and 
the  globe  is  rectified. 

The  reason  is,  that  the  shadow  of  the  axis  re¬ 
presents  an  hour  circle ;  and  by  it’s  agreement 
in  the  same  hour,  which  the  shadow  of  the  azi¬ 
muth  string  points  out,  by  it’s  intersection  on 
the  parallel  of  the  day,  it  shews  the  sun  to  be  in 
the  plane  of  the  said  parallel ;  which  can  never 
happen  in  the  morning  on  the  eastern  side  of 
the  globe,  nor  in  the  evening  on  the  western  side 
of  it,  but  when  the  globe  is  rectified. 

297 


M2 


description  and  use 


This  rectification  of  the  globe  is  only  placing 
it  in  such  a  manner,  that  the  principal  great 
circles  and  points  may  concur  and  fall  in  with 
those  of  the  heavens. 

The  many  advantages  arising  from  these  prob¬ 
lems,  relating  to  the  placing  of  the  globe  in  the 
sun’s  rays,  the  tutor  will  easily  discern,  and 
readily  extend  to  his  own,  as  well  as  to  the 
benefit  of  his  pupil. 


THE 


GENERAL  PRINCIPLES 


or 


DIALLING 


ILLUSTRATED 


BY  THE  TERRESTRIAL  GLOBE. 

HE  art  of  dialling  is  of  very  ancient  origin, 


JL  and  was  in  former  times  cultivated  by  all 
who  had  any  pretensions  to  science  \  and  before 
the  invention  of  clocks  and  watches  it  was  of  the 
highest  importance,  and  is  even  now  used  to 
correct  and  regulate  them. 

It  teaches  us,  by  means  of  the  sun’s  rays, 
to  divide  time  into  equal  parts,  and  to  repre- 


298 


OF  THE  GLOBES. 


113 


sent  on  any  given  surface  the  different  circles 
into  which,  for  convenience,  we  suppose  the 
heavens  to  be  divided,  but  principally  the  hour 
circles. 

The  hours  are  marked  upon  a  plane,  and 
pointed  out  by  the  interposition  of  a  body  which 
receiving  the  light  of  the  sun,  casts  a  shadow 
upon  the  plane.  This  body  is  called  the  axis, 
when  it  is  parallel  to  the  axis  of  the  world.  It 
is  called  the  stile,  when  it  is  so  placed  that  only 
the  end  of  it  coincides  with  the  axis  of  the  earth ; 
in  this  case,  it  is  only  this  point  which  marks  the 
hours. 

Among  the  various  pleasing  and  profitable 
amusements  which  arise  from  the  use  of  globes, 
that  of  dialling  is  not  the  least.  By  it  the  pupil 
will  gain  satisfactory  ideas  of  the  principles  on 
which  this  branch  of  science  is  founded  ;  and  it 
will  reward,  with  abundance  of  pleasure,  those 
that  chuse  to  exercise  themselves  in  the  practice 
of  it. 

If  we  imagine  the  hour  circles  of  any  place, 
as  London,  to  be  drawn  upon  the  globe  of  the 
earth,  and  suppose  this  globe  to  be  transparent, 
and  to  revolve  round  a  real  axis,  which  is  opake, 
and  casts  a  shadow  ;  it  is  evident,  that  when¬ 
ever  the  plane  of  any  hour  semicircle  points  at 
the  sun,  the  shadow  of  the  axis  will  fall  upon 
the  opposite  semicircle.* 

*  Long’s  Astronomy,  vol  i,  page  82. 

P  299 


114 


description  and  use 


Let  a  PC  p,  fig.  i,  plate  XIII,  represent  a 
transparent  globe ;  a  b  c  d  e  f  g  the  hour  semi¬ 
circles  ;  it  is  clear,  that  if  the  semicircle  Pap 
points  at  the  sun,  the  shadow  of  the  axis  will 
fall  upon  the  opposite  semicircle. 

If  we  imagine  any  plane  to  pass  through  the 
center  of  this  transparent  globe,  the  shadow  of 
half  the  axis  will  always  fall  upon  one  side  or 
the  other  of  this  intersecting  plane. 

Thus  let  ABCD  be  the  plane  of  the  hori¬ 
zon  of  London ;  so  long  as  the  sun  is  above  the 
horizon,  the  shadow  of  the  upper  half  of  the 
axis  will  fall  somewhere  upon  the  upper  side  of 
the  plane  A  B  CD;  when  the  sun  is  below  the 
horizon  of  London,  then  the  shadow  of  the 
lower  half  of  the  axis  E  falls  upon  the  lower 
side  of  the  plane. 

When  the  plane  of  any  hour  semicircle  points 
at  the  sun,  the  shadow  of  the  axis  marks  the 
respective  hour-line  upon  the  intersecting  plane. 
The  hour- line  is  therefore  a  line  drawn  from 
the  center  of  the  intersecting  plane,  to  that  point 
where  this  plane  is  cut  by  the  semicircle  oppo¬ 
site  to  the  hour  semicircle. 

Thus  let  A  B  C  D,  fig.  i,  plate  XIII,  the 
horizon  of  London,  be  the  intersecting  plane ; 
when  the  meridian  of  London  points  at  the 
sun,  as  in  the  present  figure,  the  shadow  of  the 
half  axis  P  E  falls  upon  the  line  E  B,  which  is 
drawn  from  E,  the  center  ol  the  horizon,  to 

300 


OF  THE  GLOBES.  115 

% 

the  point  where  the  horizon  is  cut  by  the  oppo¬ 
site  semicircle ;  therefore,  E  B  is  the  line  for 
the  hour  of  twelve  at  noon. 

By  the  same  method  the  rest  of  the  hour¬ 
lines  are  found,  by  drawing  for  every  hour  a 
line,  from  the  center  of  the  intersecting  plane, 
to  that  semicircle  which  is  opposite  to  the  hour 
semicircle. 

Thus  fig.  2,  plate  XIII,  shews  the  hour-lines 
drawn  upon  the  plane  of  the  horizon  of  London, 
with  only  so  many  hours  as  are  necessary ;  that 
is,  those  hours,  during  which  the  sun  is  above 
the  horizon  of  London,  on  the  longest  day  in 
summer. 

If,  when  the  hour-lines  are  thus  found,  the 
semicircles  be  taken  away,  as  the  scaffolding  is 
when  the  house  is  built,  what  remains,  as  in 
fig.  2,  will  be  an  horizontal  dial  for  London. 

If,  instead  of  twelve  hour  circles,  as  above 
described,  we  take  twice  that  number,  we  may 
by  the  points,  where  the  intersecting  plane  is 
cut  by  them,  find  the  lines  for  every  half  hour  y 
if  we  take  four  times  the  number  of  hour  cir¬ 
cles,  we  may  find  the  lines  for  every  quarter  of 
an  hour,  and  so  on  progressively. 

We  have  hitherto  considered  the  horizon  of 
London  as  the  intersecting  plane,  by  which  is 
seen  the  method  of  making  an  horizontal  dial. 
If  we  take  any  other  plane  for  the  intersecting 
plane,  and  find  the  points  where  the  hour  semi¬ 
circles  pass  through  it,  and  draw  the  lines  from 

.301 


110- 


DESCRIPTION  AND  USE 


the  center  of  the  plane  to  those  points,  we  shall 
have  the  hour-lines  for  that  plane. 

Fig.  3,  plate  XIII,  shews  how  the  hour-lines 
are  found  upon  a  south  plane,  perpendicular  to 
the  horizon.  Fig.  4,  shews  a  south  dial,  with 
it’s  hour-lines,  without  the  semicircle,  by  means 
whereof  they  are  found. 

The  gnomon  of  every  sun-dial  represents  the 
axis  of  the  earth,  and  is  therefore  always  placed 
parallel  to  it ;  whether  it  be  a  wire,  as  in  the 
figure  before  us,  or  the  edge  of  a  brass  plate,  as 
in  a  common  horizontal  dial. 

The  whole  earth,  as  to  it’s  bulk,  is  but  a 
point ,  if  compared  to  it’s  distance  from  the  sun  ; 
therefore,  if  a  small  sphere  of  glass  be  placed  on 
any  part  of  the  earth's  surface,  so  that  it's  axis 
be  parallel  to  the  axis  of  the  earth,  and  the 
sphere  have  such  lines  upon  it,  and  such  planes 
within  it,  as  above  described,  it  will  shew  the 
hour  of  the  day  as  truly  as  if  it  were  placed  at 
the  center  of  the  earth,  and  the  shell  of  the  earth 
were  as  transparent  as  glass. 

A  wire  sphere ,  with  a  thin  flat  plate  of  brass 
within  it,  is  often  made  use  of  to  explain  the 
principles  of  dialling. 

From  what  has  been  said,  it  is  clear  that 
dialling  depends  on  finding  where  the  shadow 
of  a  strait  wire,  parallel  to  the  axis  of  the 
earth,  will  fall  upon  a  given  plane,  every  hour, 
half  hour,  &c.  the  hour-lines  being  found  as 

302 


OF  THE  GLOBES. 


117 


above  described,  which  we  shall  proceed  to  ex¬ 
emplify  by  the  globe. 

Every  dial-plane  (that  is,  the  plane  surface 
on  which  a  dial  is  drawn)  represents  the  plane 
of  a  great  circle,  which  circle  is  an  horizon  to 
some  country  or  other. 

The  center  of  the  dial  represents  the  center 
of  the  earth  ;  and  the  gnomon  which  casts  the 
shade  represents  the  axis,  and  ought  to  point  • 
directly  to  the  poles  of  the  equator. 

The  plane  upon  which  dials  are  delineated 
may  be  either,  1.  parallel  to  the  horizon;  2. 
perpendicular  to  the  horizon ;  or,  3.  cutting  it 
at  oblique  angles. 

PROBLEM.  XL. 

To  construct  an  horizontal  dial  for  any  given  lati¬ 
tude ,  by  means  of  the  terrestrial  globe . 

Elevate  the  globe  to  the  latitude  of  the 
place,  then  bring  the  first  meridian  under  the 
graduated  edge  of  the  strong  brazen  one,  which 
will  then  be  over  the  hour  XII,  or  the  equator. 
As  our  globes  have  meridians  drawn  through 
every  fifteen  degrees  of  the  equator,  these  me¬ 
ridians  will  represent  the  true  circles  of  the 
sphere,  and  will  intersect  the  horizon  of  the 
globe,  in  certain  points  on  each  side  of  the  me¬ 
ridian.  The  distance  of  these  points  from  the 
meridian  must  be  carefully  noted  down  upon  a 

303 


DESCRIPTION  AND  USE 


118 

piece. of  paper,  as  will  be  seen  in  the  example. 
The  pupil  need  not,  however,  take  out  into  his 
table  the  distances  further  than  from  XII  to  VI, 
which  is  just  90  degrees ;  for  the  distances  of 
XI,  X,  IX,  VIII,  VII,  VI,  in  the  forenoon,  are 
the  same  from  XII  as  the  distances  of  I,  II, 
III,  IV,  V,  VI,  in  the  afternoon  ;  and  these 
hour-lines  continued  through  the  center  will 
give  the  opposite  hour-lines  on  the  other  half  of 
the  dial. 

No  more  hour-lines  need  be  drawn  than 
what  answer  to  the  sun’s  continuance  above  the 
horizon,  on  the  longest  day  of  the  year,  in  the 
given  latitude. 

Example .  Suppose  the  given  place  to  be 
London,  whose  latitude  is  51  deg.  SO  min. 
north. 

Elevate  the  north  pole  of  the  globe  to  5l{ 
degrees  above  the  horizon  ;  then  will  the  axis 
of  the  globe  have  the  same  elevation  above  the 
broad  paper  circle,  as  the  gnomon  of  the  dial  is 
to  have  above  the  plane  thereof. 

I  urn  the  globe,  till  the  first  meridian  (which 
on  English  globes  passes  through  London)  is 
unciei  the  graduated  side  of  the  strong  brazen 
meridian ;  then  observe  and  note  the  points 
where  the  hour-circles  intersect  the  horizon  ;  and 
as  on  our  globes  the  inner  graduated  circle,  on 
the  broad  paper  circle,  begins  from  the  two  sixes, 

east  ar)d  west,  we  shall  begin  from  thence, 

804 


OF  THE  GLOBES. 


1  19 


calling  the  hour  -  -  -  VI  0°  O 

we  shall  find  the  other  hours  intersecting  the 
horizon  at  the  following  degrees:  V  18°  54 

IV  36  24 
III  51  57 
II  65  41 
I  78  9 

» 

which  are  the  respective  distances  of  the  above 
hours  from  VI  upon  the  plane  of  the  horizon. 

To  transfer  these,  and  the  rest  of  the  hours, 
upon  an  horizontal  plane,  draw  the  parallel 
right  lines  a  c  and  b  d,  fig.  5,  plate  XIII,  upon 
that  plane,  as  far  from  each  other  as  is  equal  to 
the  intended  thickness  of  the  gnomon  of  the 
dial,  and  the  space  included  between  them  will 
be  the  meridian,  or  twelve  o’clock  line  upon  the 
dial ;  cross  this  meridian  at  right  angles  by  the 
line  g  h,  which  will  be  the  six  o’clock  line  ;  then 
setting  one  foot  of  your  compasses  in  the  inter¬ 
section  a,  describe  the  quadrant  g  e  with  any 
convenient  radius,  or  opening  of  the  compasses; 
after  this,  set  one  foot  of  the  compasses  in  the 
intersection  b,  as  a  center,  and  with  the  same 
radius  describe  the  quadrant  f  h ;  then  divide 
each  quadrant  into  90  equal  parts,  or  degrees, 
as  in  the  figure. 

Because  the  hour-lines  are  less  distant  from 
each  other  about  noon,  than  in  any  other  part 
of  the  dial,  it  is  best  to  have  the  centers  of  the 
quadrants  at  some  distance  from  the  center  of 

305 


120 


description  and  use 


the  dial-plan£,  in  order  to  enlarge  the  hour-dis¬ 
tances  near  XII ;  thus  the  center  of  the  plane 

«  * 

is  at  A,  but  the  center  of  the  quadrants  is  at  a 
and  b. 

Lay  a  rule  over  78°  9',  and  the  center  b, 
and  draw  there  the  hour-line  of  I.  Through  b, 
and  65  41,  gives  the  hour-line  of  II.  Through 
b,  and  51  57,  that  of  III.  Through  the  same 
center,  and  36  24,  we  obtain  the  hour-line  of 
IV.  And  through  it,  and  18  54,  that  of  V. 
And  because  the  sun  rises  about  four  in  the 
morning,  continue  the  hour-lines  of  IV  and  V 
in  the  afternoon,  through  the  center  T>  to  the 
opposite  side  of  the  dial. 

Now  lay  a  rule  successively  to  the  center  a 
of  the  quadrant  e  g,  and  the  like  elevations  or 
degrees  of  that  quadrant,  78  9,  65  41,  51  57, 
36  24,  18  54,  which  will  give  the  forenoon 
hours  of  XI,  X,  IX,  VIII,  and  VII ;  and  be¬ 
cause  the  sun  does  not  set  before  VIII  in  the 
evening  on  the  longest  days,  continue  the  hour¬ 
lines  of  VII  and  VIII  in  the  afternoon,  and  all 
the  hour  lines  will  be  finished  on  this  dial. 

m 

Lastly,  through  51 J  degrees  on  either  quad¬ 
rant,  and  from  it’s  center,  draw  the  right  line 
a  g  for  the  axis  of  the  gnomon  a  g  i,  and  from 
g  let  fall  the  perpendicular  g  i  upon  the  meri¬ 
dian  line  a  i,  and  there  will  be  a  triangle  made^ 
whose  sides  are  a  g,  g  i,  and  i  a ;  if  a  plate  simi¬ 
lar  to  this  triangle  be  made  as  thick  as  the  dis- 

306 


OF  ''THE  GLOBES. 


121 


tance  between  the  lines  a  c  and  b  d,  and  be  set 
upright  between  them,  touching  at  a  and  b,  the 
line  a  g  will,  when  it  is  truly  set,  be  parallel  to 
the  axis  of  the  world,  and  will  cast  a  shadow  on 
the  hour  of  the  day. 

The  trouble  of  dividing  the  two  quadrants 
may  be  saved,  by  using  a  line  of  chords,  which 
is  always  placed  upon  every  scale  belonging  to 
a  case  of  instruments. 

PROBLEM  XLI. 

To  delineate  a  direct  south  dial  for  any  given  lati¬ 
tude. )  by  the  globe . 

Let  us  suppose  a  south  dial  for  the  latitude 
of  London. 

Elevate  the  pole  to  the  co-latitude  of  your 
place,  and  proceed  in  all  respects  as  above  taught 
for  the  horizontal  dial,  from  VI  in  the  morning 
to  VI  in  the  afternoon,  only  the  hours  must  be 
reversed,  as  in  fig.  3,  plate  XIII ;  and  the  hypo- 
thenuse  a  g  of  the  gnomon  a  g  f ,  must  make  an 
angle  with  the  dial  plane  to  the  co-latitude  of  the 
place. 

As  the  sun  can  shine  no  longer  than  from  VI 
in  the  morning  to  VI  in  the  evening,  there  is  no 
occasion  for  having  more  than  twelve  hours  upon 
this  dial. 

In  solving  this  problem,  we  have  considered 
our  vertical  south  dial  for  the  latitude  of  Lon- 

O  307 

A/ 


122 


DESCRIPTION  AND  USE 


don,  as  an  horizontal  one  for  the  complement  of 
that  latitude,  or  38  deg.  30  min. ;  all  direct 
vertical  dials  may  be  thus  reduced  to  horizontal 
ones,  in  the  same  manner.  The  reason  of  this 
will  be  evident,  if  the  globe  be  elevated  to  the 
latitude  of  London ;  for  by  fixing  the  quadrant 
of  altitude  to  rhe  zenith,  and  bringing  it  to  in¬ 
tersect  the  horizon  in  the  east  point,  it  will 
point  out  the  plane  of  the  proposed  dial. 

This  p-ane  is  at  right  angles  to  the  meridian, 
and  perpendicular  to  the  horizon  ;  and  it  is  clear, 
from  the  bare  inspection  of  the  globe  thus  ele¬ 
vated,  that  it’s  axis  forms  an  angle  with  this 
plane,  which  is  just  the  complement  of  that  which 
it  forms  with  the  horizon,  and  is  therefore  just 
equal  to  the  co-latitude  of  the  place  ;  and  that 
therefore  it  is  most  simple  to  rectify  the  globe  to 
that  co-latitude. 

The  north  vertical  dial  is  the  same  with  the 
south,  only  the  stile  must  point  upwards,  and 
that  many  of  the  hours  from  it’s  direction  can 
be  of  no  use. 


PROBLEM  XLII. 

To  make  an  ere  el  dial ,  declining  from  the  south 
towards  the  east  or  west . 


Elevate  the  pole  to  the  latitude  of  the  place, 
and  screw  the  quadrant  of  altitude  to  the  zenith. 

308 


OF  THE  GLOBES.  123 

Then  if  your  dial  declines  towards  the  east, 
(which  we  shall  suppose  in  the  present  instance) 
count  in  the  horizon  the  degrees  of  declination 
from  the  east  point  towards  the  north,  and  bring 
the  lower  end  of  the  quadrant  to  coincide  with 
that  degree  of  declination  at  which  the  reckon¬ 
ing  ends. 

Then  bring  the  first  meridian  under  the  gra¬ 
duated  edge  of  the  strong  brass  meridian,  which 
strong  meridian  will  be  the  horary  index. 

Now  turn  the  globe  westward,  and  observe 
the  degrees  cut  in  the  quadrant  of  altitude  by  the 
first  meridian,  while  the  hours  XI,  X,  IX,  &c. 
in  the  forenoon,  pass  successively  under  the 
brazen  one ;  and  the  degrees  thus  cut  on  the 
quadrant  by  the  first  meridian,  are  the  respec¬ 
tive  distances  of  the  forenoon  hours,  from  XII, 
on  the  plane  of  the  quadrant. 

For  the  afternoon  hours,  turn  the  quadrant  of 
altitude  round  the  zenith,  until  it  comes  to  the 
degree  in  the  horizon,  opposite  to  that  where  it 
was  placed  before,  namely,  as  far  from  the  west 
towards  the  south,  and  turn  the  globe  eastward  ; 
and  as  the  hours  I,  II,  III,  he,  pass  under  the 
strong  brazen  meridian,  the  first  meridian  will 
cut  on  the  quadrant  of  altitude  the  number  of 
degrees  from  the  zenith,  that  each  of  the  hours 
is  from  XII  on  the  dial. 

When  the  first  meridian  goes  off  the  quad- 

309 


124 


DESCRIPTION  AND  USE 


rant  at  the  horizon,  in  the  forenoon,  the  hour 
index  will  shew  the  time  when  the  sun  comes 
upon  this  dial ;  and  when  it  goes  off  the  quad¬ 
rant  in  the  afternoon,  it  points  to  the  time  when 
the  sun  leaves  the  dial. 

Having  thus  found  all  the  hour  distances 
from  XII,  lay  them  down  upon  your  dial  plane, 
either  by  dividing  a  semicircle  into  two  quad¬ 
rants,  or  bv  the  line  of  chords. 

In  all  declining  dials,  the  line  on  which  the 
gnomon  stands  makes  an  angle  with  the  twelve 
o’clock  line,  ,and  falls  among  the  forenoon  hour 
lines,  if  the  dial  declines  towards  the  east ;  and 
among  the  afternoon  hour  lines,  when  the  dial 
declines  towards  the  west ;  that  is,  to  the  left 
hand  from  the  twelve  o’clock  line  in  the  former 
case,  and  to  the  right  hand  from  it  in  the  latter. 

To  find  the  distance  of  this  line  from  that  of 

twelve . 

This  may  be  considered,  1.  If  the  dial  de¬ 
clines  from  the  south  towards  the  east,  then 
count  the  degrees  of  that  declination  in  the  ho¬ 
rizon,  from  the  east  point  towards  the  north, 
and  bring  the  lower  end  of  the  quadrant  to 
that  degree  of  declination  where  the  reckon¬ 
ing  ends ;  then  turn  the  globe,  until  the  first 
meridian  cuts  the  horizon  in  the  like  number 

310 


OF  THE  GLOBES. 


125 


©i  degrees,  counted  from  the  south  point  to¬ 
wards  the  east,  and  the  quadrant  and  first  meri¬ 
dian  will  cross  one  another  at  right  angles,  and 
the  number  of  degrees  of  the  quadrant,  which 
are  intercepted  between  the  first  meridian  and 
the  zenith,  is  equal  to  the  distance  of  this  line 
from  the  twelve  o’clock  line. 

The  numbers  of  the  first  meridian,  which  are 
intercepted  between  the  quadrant  and  the  north 
pole,  is  equal  to  the  elevation  of  the  stile  above 
the  plane  of  the  dial. 

The  second  case  is,  when  the  dial  declines 
westward  from  the  south. 

Count  the  declination  from  the  east  point  of 
the  horizon,  towards  the  south,  and  bring  the 
quadrant  of  altitude  to  the  degree  in  the  horizon, 
at  which  the  reckoning  ends,  both  for  finding 
the  forenoon  hours,  and  the  distance  of  the  sub¬ 
stile,  or  gnomon  line,  from  the  meridian  ;  and  for 
the  afternoon  hours,  bring  the  quadrant  to  the 
opposite  degrees  in  the  horizon,  namely,  as  far 
from  the  west  towards  the  north,  and  then  pro¬ 
ceed  in  all  respects  as  before. 

It  is  presumed,  that  the  foregoing  instances 
will  be  sufficient  to  illustrate  the  general  princi¬ 
ples  of  dialling,  and  to  give  the  pupil  a  general 
idea  of  that  pleasing  science  ;  lor  accurate  and 
expeditious  methods  of  constructing  dials,  we 
must  refer  him  to  treatises  written  expressly  on 
that  subject. 


311 


126 


DESCRIPTION  AND  USE 


NAVIGATION 

EXPLAINED  BY  THE  GLOBE. 

AVIG  ATION  is  the  art  of  guiding  a  ship 


-L  n|  at  sea,  from  one  place  to  another,  in  the 
safest  and  most  convenient  manner.  In  order 
to  attain  this,  four  things  are  particularly  ne- 
cessary  : 

1.  To  know  the  situation  and  distance  of 
places. 

2.  To  know  at  all  times  the  points  of  the 
compass. 

3.  To  know  the  line  which  the  ship  is  to  be 
directed  from  one  place  to  the  other. 

4.  To  know,  in  any  part  of  the  voyage,  what 
point  of  the  globe  the  ship  is  upon. 

The  knowledge  of  the  distance  and  situa¬ 
tion  of  places,  between  which  a  voyage  is  to  be 
made,  implies  not  only  a  general  knowledge  of 
geography,  but  of  several  other  particulars,  as 
the  rocks,  sands,  streights,  rivers,  &c.  near 
which  we  are  to  sail ;  the  bending  out,  or  run¬ 
ning  in  of  the  shores,  the  knowledge  of  the 
times  that  particular  winds  sets  in,  the  seasons 
when  storms  and  hurricanes  are  to  be  expected. 


OF  THE  GLOBES. 


12? 


but  especially  the  tides ;  these  and  many  other 
similar  circumstances  are  to  be  learned  from  sea 
charts,  journals,  &c.  but  chiefly  by  observation 
and  experience. 

The  second  particular  to  be  attained,  is  the 
knowledge  at  all  times  of  the  points  of  the 
compass,  where  the  ship  is.  The  ancients,  to 
whom  the  polarity  of  the  loadstone  was  un¬ 
known,  found  in  the  day-time  the  east  or  west, 
by  the  rising  or  setting  of  the  sun  ;  and  at  night, 
the  north  by  the  polar  star.  We  have  the 
advantage  of  the  mariner’s  compass,  by  which, 
at  any  time  in  the  wide  ocean,  and  the  darkest 
night,  we  know  where  the  north  is,  and  conse¬ 
quently  the  rest  of  the  points  of  the  compass. 

Indeed,  before  the  invention  of  the  mariner’s 
compass,  the  voyages  of  the  Europeans  were 
principally  confined  to  coasting  ;  but  this  for¬ 
tunate  discovery  has  enabled  the  mariner  to  ex¬ 
plore  new  seas,  and  discover  new  countries, 
which,  without  this  valuable  acquisition,  would 
probably  have  remained  for  ever  unknown. 

The  third  thing  required  to  be  known,  is 
the  line  which  a  ship  describes  upon  the  globe 
of  the  earth,  in  going  from  one  place  to  ano¬ 
ther. 

The  shortest  way  from  one  place  to  another, 
is  an  arc  of  a  great  circle,  drawn  through  the 
two  places. 


313 


128 


DESCRIPTION  AND  USE 


The  most  convenient  way  for  a  ship,  is  that 
by  which  we  may  sail  from  one  place  to  another, 
directing  the  ship  all  the  while  towards  the  same 
point  of  the  compass. 

A  ship  is  guided  by  steering  or  directing  her 
towards  some  points  of  the  compass ;  the  line 
wherein  a  ship  is  directed,  is  called  the  ship’s 
course,  which  is  named  from  the  point  towards 
which  she  sails. 

Thus  if  a  ship  sails  towards  the  north-east 
point,  her  course  is  said  to  be  N.  E. 

In  long  voyages,  a  ship’s  way  may  consist  of 
a  great  number  of  different  courses,  as  from  A 
to  B,  from  B  to  C,  and  from  C  to  D,  fig  9, 
plate  XIII ;  when  we  speak  of  a  ship’s  course, 
we  consider  one  of  these  at  a  time  ;  the  seldomer 
the  course  is  changed,  the  more  easily  the  ship 
is  directed. 

If  two  places ,  A  and  Z,  Jig.  7,  plate  XIIL 
lie  under  the  same  meridian ,  the  course  from 
the  one  side  to  the  other  is  due  north  or  south. 
Thus  let  A  Z  be  part  of  a  meridian  ;  if  A  be 
south  of  Z,  the  course  from  A  to  Z  must  be 
north,  and  the  course  from  Z  to  A  south.  This 
is  evident  from  the  nature  of  a  meridian,  that 
it  marks  upon  the  horizon  the  north  and  south 
points,  and  that  every  point  of  any  meridian  is 
north  or  south  from  every  other  point  of  it. 
From  hence  we  may  deduce  the  following  co- 

314 


OF  THE  GLOBES. 


129 


rollary  ;  that  if  a  ship  sails  due  north  or  south, 
she  will  continue  on  the  same  meridian. 

If  two  places  lie  under  the  equator ,  the 
course  from  one  to  the  other  is  an  arc  of  the 
equator,  and  is  due  east  or  west.  Thus  let  a  z, 
fig.  7,  be  a  part  of  the  equator;  if  a  be  west 
from  z,  the  course  from  a  to  z  is  east,  and  the 
course  from  z  to  a  is  west :  for  since  the  equa¬ 
tor  marks  the  east  and  west  points  upon  the 
horizon,  every  point  of  the  equator  lies  east  or 
west  of  every  other  point  of  it,  as  may  be  seen 
upon  the  globe,  by  placing  it  as  for  a  right 
sphere,  and  bringing  a  or  z,  or  any  of  the  in¬ 
termediate  points,  to  the  zenith ;  when  it  will 
be  evident,  that  if  we  are  to  go  from  one  of 
these  points  a,  to  the  other  z,  or  to  any  point 
on  the  equator,  we  must  continue  our  course 
due  east  to  arrive  at  a,  or  vice  versa.  From  hence 
we  may  deduce  this  consequence,  that  if  a  ship 
under  the  equator  sails  due  east  or  west,  she  will 
continue  under  the  equator. 

In  the  two  foregoing  cases,  the  course  being 
an  arc  of  a  great  circle,  (the  meridian  or  equator) 
is  the  shortest  and  the  most  convenient  way  it 
can  sail. 

If  two  places  lie  under  the  same  parallel ,  the 
course  from  one  to  the  other  is  due  east  or 
west ;  this  may  be  seen  upon  the  globe,  by  the 
following  method  :  bring  any  point  of  a  paral¬ 
lel  to  the  zenith,  and  stretch  a  thread  over  it, 

R  31.5 


130 


DESCRIPTION  AND  USE 


perpendicular  to  the  meridian ;  the  thread  will 
then  be  a  tangent  to  the  parallel,  and  stand  east 
and  west  from  the  point  of  contact.  Hence, 
If  a  ship  sails  in  any  parallel,  due  east  or  west, 
she  will  continue  in  the  same  parallel.  In  this 
case,  the  most  convenient  course,  though  not 
the  shortest,  from  one  to  the  other,  is  to  sail  due 
east  or  west. 

If  two  places  lie  neither  under  the  equator ,  nor 
on  the  same  meridian ,  nor  in  the  same  parallel ,  the 
most  convenient,  though  not  the  shortest,  course 
from  one  to  the  other,  is  in  a  rhumb. 

For  if  we  should  in  this  case  attempt  to  go 
the  shortest  way,  in  a  great  circle  drawn  through 
the  two  places,  we  must  be  perpetually  chang¬ 
ing  our  course.  Thus  fig.  8,  whatever  is  the 
bearing  of  Z  from  A,  the  bearings  of  all  the 
intermediate  points,  as  B,  C,  D,  E,  &c.  will  be 
different  from  it,  as  well  as  different  from  each 
other,  as  may  be  easily  seen  upon  the  globe,  by 
bringing  the  first  point  A  to  the  zenith,  and 
observing  the  bearing  of  Z  from  each  of  them. 
Thus  suppose,  when  the  globe  is  rectified  to  the 
horizon  of  A,  the  bearing  of  Z  from  A  be  north¬ 
east,  and  the  angle  of  position  of  Z,  with  regard 
to  A,  be  45  degrees ;  if  we  bring  B  to  the  ze¬ 
nith,  we  shall  have  a  different  horizon,  and  the 
bearing  and  angle  of  position  from  Z  to  B  will 
be  different  from  the  former ;  and  so  on  of  the 
other  points  C,  D,  E,  they  will  each  of  them 

316 


OF  THE  GLOBES. 


131 


have  a  different  horizon,  and  Z  will  have  a  dif¬ 
ferent  bearing  and  angle  of  position. 

From  hence  we  may  draw  this  corollary,  that 
when  two  places  lie  one  from  the  other,  towards 
a  point  not  cardinal,  if  we  sail  from  one  place 
towards  the  point  of  the  other’s  bearing,  we 
shail  never  arrive  at  the  other  place.  Thus  if  Z 
lies  north-east  from  A,  if  we  sail  from  A  towards 
the  north-east,  we  shall  never  arrive  at  Z. 

A  rhumb  upon  the  globe  is  a  line  drawn  from 
a  given  place  A,  so  as  to  cut  all  the  meridians 
it  passes  through  at  equal  angles  ;  the  rhumbs 
are  denominated  from  the  points  of  the  compass, 
in  a  different  manner  from  the  winds.  Thus, 
at  sea,  the  north-east  wind  is  that  which  blows 
from  the  north-east  point  of  the  horizon,  to¬ 
wards  the  ship  in  which  we  are ;  but  we  are  said 
to  sail  upon  the  N.  E.  rhumb,  when  we  go  to¬ 
wards  the  north-east. 

The  rhumb  A  B  C  D  Z,  fig.  8,  plate  XIIL 
passing  through  the  meridians  L  M,  N  O,  P  Q, 
makes  the  angles  L  A  B,  N  B  C,  P  C  D,  equal ; 
from  whence  it  follows,  that  the  direction  of  a 
rhumb  is  in  every  part  of  it  towards  the  same 
point  of  the  compass ;  thus  from  every  point  of 
a  north-east  rhumb  upon  the  globe,  the  direction 
is  towards  the  north-east,  and  that  rhumb  makes 
an  angle  of  45  deg.  with  every  meridian  it  h 
drawn  through. 


317 


J  32 


DESCRIPTION  AND  USE 


Another  property  of  the  rhumbs  is,  that  equal 
parts  of  the  same  rhumb  are  contained  between 
parallels  of  equal  distance  of  latitude  ;  so  that  a 
ship  continuing  in  the  same  rhumb,  will  run  the 
same  number  of  miles  in  sailing  from  the  paral¬ 
lel  of  10  to  the  parallel  of  30,  as  she  does  in  sail¬ 
ing  from  the  parallel  of  30  to  that  of  50. 

The  fourth  thing  mentioned  to  be  required 
in  navigation,  was,  to  know  at  any  time  what 
point  of  the  globe  a  ship  is  upon.  This  depends 
upon  four  things:  1.  the  longitude;  2.  the 
latitude  ;  3.  the  course  the  ship  has  run  ;  4.  the 
distance,  that  is,  the  way  she  has  made,  or  the 
number  of  leagues  or  miles  she  has  run  in  that 
course,  from  the  place  of  the  last  observation. 
Now  any  two  of  these  being  known,  the  rest  may 
be  easily  found. 

Having  thus  given  some  general  idea  of 
navigation,  we  now  proceed  to  the  problems 
by  which  the  cases  of  sailing  are  solved  on  the 
globe. 


PROBLEM  XLTII. 

Given  the  difference  of  latitude ,  and  difference  of 
longitude ,  to  find  the  coune  and  distance  sailed ,* 

Example .  Admit  a  ship  sails  from  a  port 


*  See  Martin  on  the  Globes. 
318 


OF  THE  GLOBES. 


133 


A,  in  latitude  38  deg.  to  another  port  B,  in 
latitude  5  deg.  and  finds  her  difference  of  longi¬ 
tude  43  deg. 

Let  the  port  A  be  brought  to  the  meridian, 
and  elevate  the  globe  to  the  given  latitude  of  that 
port  38  deg.  and  fixing  the  quadrant  of  altitude 
precisely  over  it  on  the  meridian,  move  the  quad¬ 
rant  to  lie  over  the  second  port  B,  (found  by  the 
given  difference  of  latitude  and  longitude)  then 
will  iucut  in  the  horizon  50  deg.  45  min.  for 
the  angle  of  the  ship's  course  to  be  steered  from 
the  port  A.  Also,  count  the  degrees  in  the 
quadrant  between  the  two  ports,  which  you  will 
find  51  deg.;  this  number  multiplied  by  60, 
(the  nautical  miles  in  a  degree)  will  give  3060 
for  the  distance  run. 


PROBLEM  XLI V. 

Given  the  difference  of  latitude  and  course ,  to  find 
the  difference  of  longitude  and  distance  sailed . 

Example,  Admit  a  ship  sails  from  a  port  A, 
in  25  deg.  north  latitude,  to  another  port  B,  in 
30  deg.  south  latitude,  upon  a  course  of  43  deg. 

Bring  the  port  A  to  the  meridian,  and  rec¬ 
tify  the  globe  to  the  latitude  thereof  25  deg. 
where  fix  the  quadrant  of  altitude,  and  place  it 
to  make  an  angle  with  the  meridian  of 

319 


so  as 


134 


DESCRIPTION  AND  USE 


43  deg.  in  the  horizon,  and  observe  where  the 
edge  of  the  quadrant  intersects  the  parallel  of 
30  deg.  south  latitude,  for  that  is  the  place  of 
the  port  B.  Then  count  the  number  of  degrees 
on  the  edge  of  the  quadrant  intersected  between 
the  two  ports,  and  there  will  be  found  73  deg* 
which,  multiplied  by  60,  gives  4380  miles  for 
the  distance  sailed.  As  the  two  ports  are  now 
known,  let  each  be  brought  to  the  meridian,  and 
observe  the  difference  of  longitude  in  the  equa¬ 
tor  respectively,  which  will  be  found  50  degrees. 

N.  B.  Had  this  problem  been  solved  by 
loxodromics ,  or  sailing  on  a  rhumb,  the  differ¬ 
ence  of  longitude  would  then  have  been  52  deg. 
30  min.  between  the  two  ports. 

PROBLEM  XLV. 

Given  the  difference  of  latitude  and  distance  run , 
to  find  the  difference  of  longitude ,  and  angle  of 
the  course . 

Example .  Admit  a  ship  sails  from  a  port 
A,  in  latitude  50  deg.  to  another  port  B,  in 
latitude  17  deg.  30  min.  and  her  distance  run 
be  2220  miles.  Rectify  the  globe  to  the  lati¬ 
tude  of  the  place  A,  then  the  distance  run,  re- 
duced  to  degrees,  will  make  37  deg.  which  are 
to  be  reckoned  from  the  end  of  the  quadrant 
lying  over  the  port  A,  under  the  meridian  5 

320 


OF  THE  GLOBES. 


135 


then  is  the  quadrant  to  be  moved,  till  the  37 
deg.  coincides  with  the  parallel  of  17  deg.  30 
min.  north  latitude ;  then  will  the  angle  of  the 
course  appear  in  the  arch  of  the  horizon,  inter¬ 
cepted  between  the  quadrant  and  the  meridian, 
which  will  be  32  deg.  40  min. ;  and  by  making 
a  mark  on  the  globe  for  the  port  B,  and  bring¬ 
ing  the  same  to  the  meridian,  you  wiil  observe 
what  number  of  degrees  pass  under  the  meridian, 
which  will  be  20,  the  difference  of  longitude 
required. 


PROBLEM  XLYI. 

Given  the  difference  of  longitude  and  course ,  to 
find  the  difference  of  latitude  and  distance  sail - 
ed. 

Example.  Suppose  a  ship  sails  from  A,  in 
the  latitude  51  deg.  on  a  course  making  an 
angle  with  the  meridian  of  40  deg.  till  the  dif¬ 
ference  of  longitude  be  found  just  20  deg. ; 
then  rectifying  the  globe  to  the  latitude  of  the 
port  A,  place  the  quadrant  of  altitude  so  as  to 
make  an  angle  of  40  deg.  with  the  meridian ; 
then  observe  at  what  point  it  intersects  the 
meridian  passing  through  the  given  longitude 
of  the  port  B,  and  there  make  a  mark  to  repre¬ 
sent  the  said  port ;  then  the  number  of  degrees 
intercepted  between  that  and  the  port  A  will 
be  28,  which  will  give  ]680  miles  for  the  dis- 

312 


136 


description  and  use 


tance  run.  And  the  said  mark  for  the  port  B, 
being  brought  to  the  meridian,  will  have  it’s 
latitude  there  shewn  to  be  27  deg.  40  min. 

PROBLEM  XL VII. 

Given  the  course  and  distance  sailed ,  to  find  the 
difference  of  longitude ,  and  difference  of  lati¬ 
tude. 

Example.  Suppose  a  ship  sails  1800  miles 
from  a  port  A,  51  deg.  15  min,  south-west,  on. 
an  angle  of  45  deg.  to  another  port  B. 

Having  rectified  the  globe  to  the  port  A,  fix 
the  quadrant  of  altitude  over  it  in  the  zenith, 
and  place  it  to  the  south-west  point  in  the  hori¬ 
zon  ;  then  upon  the  edge  of  the  quadrant  under 
30  deg.  (equal  to  1 800  miles  from  the  port  A) 
is  the  port  B  ;  which  bring  to  the  meridian,  and 
you  will  there  see  the  latitude ;  and  at  the  same 
time,  it’s  longitude  on  the  equator,  in  the  point 
cut  by  the  meridian. 

In  all  these  cases,  the  ship  is  supposed  to  be 
kept  upon  the  arch  of  a  great  circle ,  which  is 
not  difficult  to  be  done,  very  nearly,  by  means 
of  the  globe,  by  frequently  observing  the  lati¬ 
tude,  measuring  the  distance  sailed,  and  (when 
you  can)  finding  the  difference  of  longitude ; 
for  one  of  these  being  given,  the  place  and 
course  of  the  ship  is  known  at  the  same  time ; 
and  therefore  the  preceding,  course  may  be  al- 

322 


i 


OF  THE  GLOBES, 


13? 


tered,  and  rectified  without  any  trouble,  through 
the  whole  voyage,  as  often  as  such  observations 
can  be  obtained,  or  it  is  found  necessary.  Now 
if  any  of  these  data  are  but  of  the  quantity  of 
four  or  five  degrees,  it  will  suffice  for  correcting 
the  ship’s  course  by  the  globe,  and  carrying  her 
directly  to  the  intended  port,  according  to  the 
following  problem. 

PROBLEM  XLVIII. 

To  steer  a  ship  upon  the  arch  of  a  great  circle  by 
the  given  difference  of  latitude ,  or  difference  of 
longitude ,  or  distance  sailed  in  a  given  time . 

Admit  a  ship  sails  from  a  port  A,  to  a  very 
distant  port  Z,  whose  latitude  and  longitude  are 
given,  as  well  as  it’s  geographical  bearing  from 
A  ;  then. 

First,  having  rectified  the  globe  to  the  port  A, 
lay  the  quadrant  of  altitude  over  the  port  Z,  and 
draw  thereby  the  arch  of  the  great  circle  through 
A  and  Z  ;  this  will  design  the  intended  path  or 
tract  of  the  ship. 

Secondly,  having  kept  the  ship  upon  the 
first  given  course  for  some  time,  suppose  by  an 
observation  you  find  the  latitude  of  the  present 
place  of  the  ship,  this  added  to,  or  subducted 
from  the  latitude  of  the  port  A,  will  give  the 
present  latitude  in  the  meridian  \  to  which 

S  323 


138 


DESCRIPTION  AND  USE 


bring  the  path  of  the  ship,  and  the  part  therein, 
which  lies  under  the  new  latitude,  is  the  true 
place  B  of  the  ship  in  the  great  arch.  To  the 
latitude  of  B  rectify  the  globe,  and  lay  the  quad¬ 
rant  over  Z,  and  it  will  shew  in  the  horizon  the 
new  course  to  be  steered. 

Thirdly,  suppose  the  ship  to  be  steered  upon 
this  course,  till  her  distance  run  be  found  300  - 
miles,  or  5  deg. ;  then,  the  globe  being  rectified 
to  the  place  B  in  the  zenith,  laying  the  quadrant 
from  thence  over  the  great  arch,  make  a  mark 
at  the  5th  degree  from  B,  and  that  will  be  the 
present  place  of  the  ship,  which  call  C  ;  which 
being  brought  to  the  meridian,  it’s  latitude  and 
longitude  will  be  known.  Then  rectify  the 
globe  to  the  place  C,  and  laying  the  quadrant 
from  thence  to  Z,  the  new  course  to  be  steered 
will  appear  in  the  horizon. 

Fourthly,  having  steered  some  time  upon 
this  new  course,  suppose,  by  some  means  or 
other,  you  come  to  know  the  difference  of  longi¬ 
tude  of  the  present  place  of  the  ship,  and  of  any 
of  the  preceding  places,  C,  B,  A;  as  B,  for 
instance  ;  then  bring  B  to  the  meridian,  and 
turn  the  globe  about,  till  so  many  degrees  of 
the  equator  pass  under  the  meridian  as  are 
equal  to  the  discovered  distance  of  longitude  ; 
then  the  point  of  the  great  arch  cut  by  the  me¬ 
ridian  is  the  present  place  D  of  the  ship,  to 

324 


OF  THE  GLOBES, 


139 


which  the  new  course  is  to  be  found  as  be¬ 
fore. 

And  thus,  by  repeating  these  observations  at 
proper  intervals,  you  will  find  future  places, 
E,  F,  G,  &c.  in  the  great  arch ;  and  by  rectify¬ 
ing  the  course  at  each,  your  ship  will  be  con¬ 
ducted  on  the  great  circle,  or  the  nearest  way 
from  the  port  A  to  Z,  by  the  use  of  the  globe 
mi  ly. 


OF  THE  USE 


OF  THE 


TERRESTRIAL  GLOBE, 


WHEN  MOUNTED 


IN  THE  COMMON  MANNER, 


LTHOUGH  I  have,  in  the  first  part  of 


XjL  this  essay,  laid  before  my  readers  the 
reasons  which  induce  me  to  prefer  my  father’s 
manner  of  mounting  the  globes,  to  the  old  or 
Ptolemaic  form,  yet  as  many  may  be  in  posses¬ 
sion  of  globes  mounted  in  the  old  form,  and 
others  may  have  been  taught  by  those  globes,  I 
thought  it  would  render  these  essays  more  com- 


325 


140 


description  and  use 


plete,  to  give  an  account  of  so  many  of  the  lead¬ 
ing'  problems,  solved  on  the  common  globes,  as 
would  enable  them  to  apply  the  remainder  of 
those  heretofore  solved,  to  their  own  use.  This 
is  the  more  expedient,  as,  since  the  publication 
of  my  father’s  treatise,  there  have  been  a  few 
attempts  to  do  away  some  of  the  inconveniences 
of  the  ancient  form,  particular  that  of  the  old 
hour-circle,  which  is  now  generally  placed  under 
the  meridian. 

I  cannot,  however,  refrain  from  again  observ¬ 
ing  to  the  pupil,  that  the  solution  of  the  prob¬ 
lems  on  the  old  globes  depends  upon  appear¬ 
ances  ;  that  therefore,  if  he  means  to  content 
himself  with  the  mere  mechanical  solution  of 
them,  the  Ptolemaic  globes  will  answer  his  pur¬ 
pose  ;  but  it  he  wishes  to  have  clear  ideas  of  the 
rationale  of  those  problems,  he  must  use  those 
mourned  in  my  father’s  manner. 

The  celestial  globe  is  used  the  same  way  in 
both  mountings,  excepting  that  in  my  father’s 
mounting  it  has  some  additional  circles ;  but  the 
difference  is  so  trifling,  that  it  is  presumed  the 
pupil  can  find  no  difficulty  in  applying  the  direc¬ 
tions  there  given  to  the  old  form. 

326 


OF  THE  GLOBES. 


141 


PROBLEM  I. 

To  find  the  latitude  and  longitude  of  any  given  place 

on  the  globe . 

Bring  the  place  to  the  east  side  of  the  brass 
meridian,  then  the  degree  marked  on  the  meri¬ 
dian  over  it  shews  it’s  latitude,  and  the  degree 
of  the  equator  under  the  meridian  shews  it’s 
longitude.  , 

Hence,  if  the  longitude  and  latitude  of  any¬ 
place  be  given,  the  place  is  easily  found,  by 
bringing  the  given  longitude  to  the  meridian  j 
for  then  the  place' will  lie  under  the  given  de¬ 
gree  of  latitude  upon  the  meridian. 

\ 

PROBLEM  II. 

To  find  the  difference  of  longitude  between  any  two 

given  places . 

Bring  each  of  the  given  places  successively  to 
the  brazen  meridian,  and  see  where  the  meridian 
cuts  the  equator  each  time  ;  the  number  of  de¬ 
grees  contained  between  those  two  points,  if  it 
be  less  than  180  deg.  otherwise  the  remainder 
to  360  deg.  will  be  the  difference  of  longitude 
required. 


327 


142 


* 


description  and  USi 


PROBLEM  III. 

To  rectify  the  globe  for  the  latitude ,  zenith ,  and 

sun9 s  place . 

Find  the  latitude  of  the  place  by  prob.  1,  and 
if  the  place  be  in  the  northern  hemisphere,  ele¬ 
vate  the  north  pole  above  the  horizon,  according 
to  the  latitude  of  the  place.  If  the  place  be  in  the 
southern  hemisphere,  elevate  the  south  pole 
above  the  south  point  of  the  horizon,  as  many 
degrees  as  are  equal  to  the  latitude. 

Having  elevated  the  globe  according  to  it’s 
latitude,  count  the  degrees  thereof  upon  the 
meridian  from  the  equator  towards  the  elevated 
pole,  and  that  point  will  be  the  zenith,  or  the 
vertex  of  the  place  ;  to  this  point  of  the  meri¬ 
dian  fasten  the  quadrant  of  altitude,  so  that  the 
graduated  edge  thereof  may  be  joined  to  the  said 
point. 

Having  brought  the  sun’s  place  in  the  eclip¬ 
tic  to  the  meridian,  set  the  hour  index  to  twelve 
at  noon,  and  the  globe  will  be  rectified  to  the 
sun’s  place. 

328 


f 


©F  THE  GLOBES® 


143 


PROBLEM  IV. 

The  hour  of  the  day  at  any  place  being  given ,  to 
find  all  those  on  the  globe ,  where  it  is  noon ,  mid¬ 
night  ^  or  any  given  hoar  at  that  time . 

On  the  globes  when  mounted  in  the  common 
manner,  it  is  now  customary  to  place  the  hour- 
circle  under  the  north  pole ;  it  is  divided  into 
twice  twelve  hours,  and  has  two  rows  of  figures, 
one  running  from  east  to  west,  the  other  from 
west  to  east ;  this  circle  is  moveable,  and  the 
meridian  answers  the  purpose  of  an  index. 

Bring  the  given  place  to  the  brazen  meridian, 
and  the  given  hour  of  the  day  on  the  hour-circle, 
this  done,  turn  the  globe  about,  till  the  meri¬ 
dian  points  at  the  hour  desired  ;  then,  with  al! 
those  under  the  meridian,  it  is  noon,  midnight, 

or  any  given  hour  at  that  time. 

) 

♦  v  , 

PROBLEM  V. 

The  hour  of  the  day  at  any  place  being  given ,  /# 
find  the  corresponding  hour  ( or  what  oy clock  it 
is  at  that  time  J  in  any  other  place . 

Bring  the  given  place  to  the  brazen  meri¬ 
dian,  and  set  the  hour-circle  to  the  given 
time  y  then  turn  the  globe  about,  until  the 
place  where  the  hour  is  required  comes  to  the 

329 


144 


description  and  use 


meridian,  and  the  meridian  will  point  out  the 
hour  of  the  day  at  that  place. 

Thus,  when  is  is  noon  at  London,  it  is 

H.  M. 


f  Rome 

m 

0 

5  2 

P.  M. 

j  Constantinople 

M 

2 

7 

P.  M. 

l  Vera  Cruz  - 

- 

5 

30 

A.  M. 

LPekinin  China 

KB 

7 

<50 

P.  M. 

PROBLEM  VI. 

The  day  of  the  month  being  given ,  to  find  all  those 
places  on  the  globe  where  the  sun  will  be  vertical 
or  in  the  zenith ,  that  day . 

Having  found  the  sun’s  place  in  the  ecliptic 
for  the  given  day,  bring  the  same  to  the  brazen 
meridian,  observe  what  degree  of  the  meridian 
is  over  it,  then  turn  the  globe  round  it’s  axis, 
and  all  places  that  pass  under  that  degree  of  the 
meridian,  will  have  the  sun  vertical,  or  in  the 
zenith,  that  day  ;  u  e.  directly  over  the  head  of 
each  place  at  it’s  respective  noon. 

PROBLEM  VII. 

A  place  being  given  in  the  torrid  zone ,  to  find  those 
two  days  in  the  year  on  which  the  sun  will  be 
vertical  to  that  place . 

Bring  the  given  place  to  the  brazen  meri¬ 
dian,  and  mark  the  degree  of  latitude  that  is 

330 


OF  THE  GLOBES, 


145 


exactly  over  it  on  the  meridian ;  then  turn  the 
globe  about  it’s  axis,  and  observe  the  two  points 
of  the  ecliptic  which  pass  exactly  under  that  de¬ 
gree  of  latitude,  and  look  on  the  horizon  for 
the  two  days  of  the  year  in  which  the  sun  is  in 
those  points  or  degrees  of  the  ecliptic,  and  they 
are  the  days  required  ;  for  on  them,  and  none 
else,  the  sun’s  declination  is  equal  to  the  latitude 
of  the  given  place. 

PROBLEM.  VIII. 

To  find  the  antoeci ,  periceci ,  and  antipodes  of  any 

given  place , 

Bring  the  given  place  to  the  brazen  meri¬ 
dian,  and  having  found  it’s  latitude,  keep  the 
globe  in  that  position,  and  count  the  same  num¬ 
ber  of  degrees  of  latitude  on  the  meridian,  from 
the  equator  towards  the  contrary  pole,  and  where 
the  reckoning  ends,  that  will  give  the  place  of 
the  antceci  upon  the  globe.  Those  who  live  at 
the  equator  have  no  amceci. 

The  globe  remaining  in  the  same  position, 
bring  the  upper  XII  on  the  horary  circle  to  the 
meridian,  then  turn  the  globe  about  till  the  me¬ 
ridian  points  to  the  lower  XII ;  the  place  which 
then  lies  under  the  meridian,  having  the  same 
latitude  with  the  given  place,  is  the  perioeci  re¬ 
quired.  Those  who  live  at  the  poles,  ii  any, 
have  no  perioeci. 


T  331 


146 


DESCRIPTION  and  use 


As  the  globe  now  stands  (with  the  index  at 
the  lower  XII),  the  antipodes  of  the  given  place 
are  under  the  same  point  of  the  brazen  meri¬ 
dian  where  it’s  antceci  stood  before. 


PROBLEM.  IX. 

To  find,  at  what  hour  the  sun  rises  and  sets  any 
day  in  the  year ,  and  also  upon  what  point  of 
the  compass . 

Rectify  the  globe  for  the  latitude  of  the  place 
you  are  in ;  bring  the  sun’s  place  to  the  meri¬ 
dian,  and  bring  the  XII  to  the  meridian ;  then 
turn  the  sun’s  place  to  the  eastern  edge  of  the 
horizon,  and  the  meridian  will  point  out  the  hour 
of  rising ;  if  you  bring  it  to  the  western  edge 
of  the  horizon,  it  will  shew  the  setting. 

Thus  on  the  16th  day  of  March,  the  sun  rose 
a  little  past  six,  and  set  a  little  before  six. 

Note.  In  the  summer  the  sun  rises  and  sets 

» 

a  little  to  the  northward  of  the  east  and  west 
points,  but  in  winter,  a  little  to  the  southward 
of  them.  If,  therefore,  when  the  sun’s  place  is 
brought  to  the  eastern  and  western  edges  of  the 
horizon,  you  look  on  the  inner  circle,  right 
against  the  sun’s  place,  you  will  see  the  point  of 
the  compass  upon  which  the  sun  rises  and  sets 
that  day.  , 


332 


OF  THE  GLOBES. 


147 


\ 

PROBLEM.  X. 

To  find,  the  length  of  the  day  and  night  at  any  time 

of  the  year . 

Only  double  the  time  of  the  sun’s  rising  that 
day,  and  it  gives  the  length  of  the  night ;  dou¬ 
ble  the  time  of  his  setting,  and  it  gives  the  length 
of  the  day. 

This  problem  shews  how  long  the  sun  stays 
with  us  any  day,  and  how  long  he  is  absent  from 
us  any  night. 

Thus  on  the  26th  of  May  the  sun  rises  about 
four,  and  sets  about  eight ;  therefore  the  day  is 
sixteen  hours  long,  and  the  night  eight. 

9 

PROBLEM  XI. 

To  find  the  lengtJr  of  the  longest  or  shortest  day ,  at 
any  place  upon  the  earth . 

Rectify  the  globe  for  that  place,  bring  the 
beginning  of  Cancer  to  the  meridian,  bring  XII 
to  the  meridian,  then  bring  the  same  degree  of 
Cancer  to  the  east  part  of  the  horizon,  and  the 
meridian  will  shew  the  time  of  the  sun’s  rising. 

If  the  same  degree  be  brought  to  the 
western  side,  the  meridian  will  shew  the  set¬ 
ting,  which  doubled,  (as  in  the  last  problem) 

333 


148 


DESCRIPTION  AND  USE 


will  give  the  length  of  the  longest  day  and  short¬ 
est  night. 

If  we  bring  the  beginning  of  Capricorn  to 
the  meridian,  and  proceed  in  all  respects'as  be¬ 
fore,  we  shall  have  the  length  of  the  longest 
night  and  shortest  day. 

Thus  in  the  Great  Mogul’s  dominions,  the 
longest  day  is  fourteen  hours,  and  the  shortest 
night  ten  hours.  The  shortest  day  is  ten  hours, 
and  the  longest  night  fourteen  hours. 

At  Petersburgh,  the  seat  of  the  Empress  of 
Russia,  the  longest  day  is  about  192  hours,  and 
the  shortest  night  41  hours ;  the  shortest  day  4| 
hours,  and  longest  night  I9i  hours. 

Note .  In  all  places  near  the  equator,  the  sun 

rises  and  sets  at  six  the  vear  round.  From 

* 

thence  to  the  polar  circles,  the  days  increase  as 
the  latitude  increases;  so  that  at  those  circles 
themselves,  the  longest  day  is  24  hours,  and  the 
longest  night  just  the  same.  From  the  polar  cir¬ 
cles  to  the  poles,  the  days  continue  to  lengthen 
into  weeks  and  months;  so  that  at  the  very  pole, 
the  sun  shines  for  six  months  together  in  sum¬ 
mer,  and  is  absent  from  it  six  months  in  winter. 

Note .  That  when  it  is  summer  with  the  nor¬ 
thern  inhabitants,  it  is  winter  with  the  southern, 
and  the  contrary  ;  and  every  part  of  the  world 
partakes  of  an  equal  share  of  light  and  dark¬ 
ness. 


334 


OF  THE  GLOBES* 


149 


PROBLEM  XII. 

To  find  all  those  inhabitants  to  whom  the  sun  is  this 
moment  rising  or  setting ,  in  their  meridian  or 
midnight . 

Find  the  sun’s  place  in  the  ecliptic,  and  raise 
the  pole  as  much  above  the  horizon  as  the  sun 
(that  day)  declines  from  the  equator  ;  then  bring 
the  place  where  the  sun  is  vertical  at  that  hour 
to  the  brass  meridian ;  so  it  will  then  be  in  the 
zenith  or  center  of  the  horizon.  Now  see  what 
countries  lie  on  the  western  edge  of  the  horizon, 
for  in  them  the  sun  is  rising ;  to  those  on  the 
eastern  side  he  is  setting ;  to  those  under  the 
upper  part  of  the  meridian  it  is  noon  day  ;  and 
to  those  under  the  lower  part  of  it,  it  is  midnight. 

Thus  on  the  25th  of  April,  at  six  o’clock  in 
the  evening,  at  Worcester, 

The  sun  is  rising  at  New  Zealand  ;  and  to 
those  who  are  sailing  in  the  middle  of  the  Great 
South  Sea. 

The  sun  is  setting  at  Sweden,  Hungary, 
Italy,  Tunis,  in  the  middle  of  Negroland  and 
Guinea. 

In  the  meridian  (or  noon)  at  the  middle  of 
Mexico,  Bay  of  Honduras,  middle  of  Florida, 
Canada, 


335 


150 


description  and  use 


Midnight  at  the  middle  of  Tartary,  Bengal, 
India,  and  the  seas  near  the  Sunda  isles. 


PROBLEM  XIII. 


To  find  the  beginning  and  end  of  twilight . 

The  twilight  is  that  faint  light  which  opens 
the  morning  by  little  and  little  in  the  east,  be¬ 
fore  the  sun  rises ;  and  gradually  shuts  in  the 
evening  in  the  west,  after  rhe  sun  is  set.  It 
arises  from  the  sun’s  illuminating  the  upper 
part  of  the  atmosphere,  and  begins  always  when 
he  approaches  within  eighteen  degrees  of  the 
eastern  part  of  the  horizon,  and  ends  when  he 
descends  eighteen  degrees  below  the  western  ; 
when  dark  night  commences,  and  continues  till 
day  breaks  again. 

To  find  the  beginning  of  twilight,  rectify  the 
globe  ;  turn  the  degree  of  the  ecliptic,  which 
is  opposite  to  the  sun’s  place,  till  it  is  elevated 
eighteen  degrees  in  the  quadrant  of  altitude 
above  the  horizon  on  the  west,  so  will  the  in¬ 
dex  point  the  hour  twilight  begins. 

This  short  specimen  of  problems  by  the  old 
globes,  it  is  presumed,  will  be  sufficient  to  ena¬ 
ble  the  pupil  to  solve  any  other. 

336 


PART  IV. 


OF  THE  USE  OF  THE  CELESTIAL  GLOBE 


HE  celestial  globe  is  an  artificial  represen 


JSL  tation  of  the  heavens,  having  the  fixed 
stars  drawn  upon  it,  in  their  natural  order  and 
situation ;  whilst  it’s  rotation  on  it’s  aids  repre¬ 
sents  the  apparent  diurnal  motion  of  the  sun, 
moon,  and  stars. 

It  is  not  known  how  early  the  ancients  had 
any  thing  of  this  kind:  we  are  not  certain  what 
the  sphere  of  Atlas  or  Musseus  was ;  perhaps 
Palamedes,  who  lived  about  the  time  of  the 
Trojan  war,  had  something  of  this  kind  ;  for  of 
him  it  is  said. 

To  mark  the  signs  that  cloudless  skies  bestow, 

To  tell  the  seasons,  when  to  sail  and  plow, 

He  first  devised ;  each  planet’s  order  found, 

It’s  distance,  period,  in  the  blue  profound. 


33  7 


152  DESCRIPTION  and  use 

From  Pliny  it  would  seem  that  Hipparchus 
had  a  celestial  globe  with  the  stars  delineated 
upon  it. 

It  is  not  to  be  supposed  that  the  celestial 
globe  is  so  just  a  representation  of  the  heavens 
as  the  terrestrial  globe  is  of  the  earth  ;  because 
here  the  stars  are  drawn  upon  a  convex  surface, 
whereas  they  naturally  appear  in  a  concave  one. 

But  suppose  the  globe  were  made  of  glass,  then 
to  an  eye  placed  in  the  center,  the  stars  which 
are  drawn  upon  it  would  appear  in  a  concave 

surface,  just  as  they  do  in  the  heavens. 

•  r  - 

Or  if  the  reader  was  to  suppose  that  holes 
were  made  in  each  star,  and  an  eye  placed  in 
the  center  of  the  globe,  it  would  view,  through 
those  holes,  the  same  stars  in  the  heavens  that 
they  represent.  .  1 

As  the  terrestrial  globe,  by  turning  on  it’s 
axis,  represents  the  real  diurjial  motion  of  the 
earth  ;  so  the  celestial  globe,  by  turning  on  it’s 
axis,  represents  the  apparent  diurnal  motion  of 
the  heavens. 

For  the  sake  of  perspicuity,  and  to  avoid  con¬ 
tinual  references,  it  will  be  necessary  to  repeat 
here  some  articles  which  have  been  already  men¬ 
tioned. 

The  ecliptic  is  that  graduated  circle  which 
crosses  the  equator  in  an  angle  of  about  23  \  de« 

338 


OF  THE  GLOBES. 


153 


grees,  and  the  angle  is  called  the  obliquity  of  the 
ecliptic. 

This  circle  is  divided  into  twelve  equal  parts, 
consisting  of  30  degrees  each  ;  the  beginnings  of 
them  are  marked  with  characters,  representing 
the  twelve  signs. 

Aries  r,  Taurus  tf,  Gemini  n,  Cancer  s, 
Leo  St,  Virgo  t^,  Libra  Scorpio  nv?  Sagitta¬ 
rius  /,  Capricornus  itf,  Aquarius  Pisces,  x. 

Upon  my  father’s  globes,  just  under  the  eclip¬ 
tic,  the  months,  and  days  of  each  month,  are 
graduated,  for  the  readier  fixing  the  artificial 
sun  upon  it’s  place  in  the  ecliptic. 

The  two  points  where  the  ecliptic  crosses  the 
equinoctial,  (the  circle  that  answers  to  the  equa¬ 
tor  on  the  terrestrial  globe)  are  called  the  equinoc¬ 
tial  points ;  they  are  at  the  beginnings  of  Aries 
and  Libra,  and  are  so  called,  because  when  the 
sun  is  in  either  of  them,  the  day  and  night  is 
every  where  equal. 

The  first  points  of  Cancer  and  Capricorn  are 
called  solstitial  points;  because  when  the  sun 
arrives  at  either  of  them,  he  seems  to  stand  in  a 
manner  still  for  several  days,  in  respect  to  his 
distance  from  the  equinoctial ;  when  he  is  in  one 
solstitial  point,  he  makes  to  us  the  longest  day ; 
when  in  the  other,  the  longest  night. 

The  latitude  and  longitude  of  stars  are  deter¬ 
mined  from  the  ecliptic. 

U  339 


154  description  and  use 

/ 

The  longitude  of  the  stars  and  planets  is  reck¬ 
oned  upon  the  ecliptic ;  the  numbers  beginning 
at  the  first  points  of  Aries  r,  where  the  ecliptic 
crosses  the  equator,  and  increasing  according  to 
the  order  of  the  signs. 

Thus  suppose  the  sun  to  be  in  the  10th  de¬ 
gree  of  Leo,  we  say,  his  longitude,  or  place,  is 
four  signs,  ten  degrees ;  because  he  has  already 
passed  the  four  signs,  Aries,  Taurus,  Gemini* 
Cancer,  and  is  ten  degrees  in  the  fifth. 

The  latitude  of  the  stars  and  planets  is  deter¬ 
mined  by  their  distance  from  the  ecliptic  upon  a 
secondary  or  great  circle  passing  through  it’s 
poles,  and  crossing  it  at  right  angles. 

Twenty-four  of  these  circular  lines,  which 
cross  the  ecliptic  at  right  angles,  being  fifteen 
degrees  from  each  other,  are  drawn  upon  the 
surface  of  our  celestial  globe ;  which  being  pro¬ 
duced  both  ways,  those  on  one  side  meet  in  a 
point  on  the  northern  polar  circle,  and  those  on 
the  other  meet  in  a  point  on  the  southern  polar 
circle. 

The  points  determined  by  the  meeting  of  these 
circles  are  called  the  poles  of  the  ecliptic,  one 
north,  the  other  south. 

From  these  definitions  it  follows,  that  longi¬ 
tude  and  latitude,  on  the  celestial  globe,  bear 
just  the  same  relation  to  the  ecliptic,  as  they  do 
on  the  terrestrial  globe  to  the  equator. 

340 


OF  THE  GLOBES. 


1 55 


Thus  as  the  longitude  of  places  on  the  earth 
is  measured  by  degrees  upon  the  equator,  count¬ 
ing  from  the  first  meridian ;  so  the  longitude 
of  the  heavenly  bodies  is  measured  by  degrees 
upon  the  ecliptic,  counting  from  the  first  point 
of  Aries. 

And  as  latitude  on  the  earth  is  measured  by 
degrees  upon  the  meridian,  counting  from  the 
equator ;  so  the  latitude  of  the  heavenly  bodies 
is  measured  by  degrees  upon  a  circle  of  longi¬ 
tude,  counting  either  north  or  south  from  the 
ecliptic. 

The  sun ,  therefore,  has  no  latitude ,  being  al¬ 
ways  in  the  ecliptic  ;  nor  do  we  usually  speak 
of  his  longitude,  but  rather  of  his  place  in  the 
ecliptic,  expressing  it  by  such  a  degree  and 
minute  of  such  a  sign,  as  5  degrees  of  Taurus, 
instead  of  3.5  degrees  of  longitude. 

The  distance  of  any  heavenly  body  from  the 
equinoctial,  measured  upon  the  meridian,  is 
called  it’s  declination . 

Therefore,  the  sun’s  declination,  north  or 
south,  at  any  time,  is  the  same  as  the  latitude  of 
any  place  to  which  he  is  then  vertical,  which  is 
never  more  than  23  £  degrees. 

Therefore  all  parallels  of  declination  on  the 
celestial  globe  are  the  very  same  as'parallels  of 
latitude  on  the  terrestrial. 

Stars  may  have  north  latitude  and  south  decli¬ 
nation,  and  vice  versa. 


341 


156 


DESCRIPTION  AND  USE 


That  which  is  called  longitude  on  the  terres. 
trial  globe,  is  called  right  ascension  on  the  celes¬ 
tial  ;  namely,  the  sun  or  star’s  distance  from  that 
meridian  which  passes  through  the  first  point  of 
Aries,  counted  on  the  equinoctial. 

Astronomers  also  speak  of  oblique  ascension 
and  descension ,  by  which  they  mean  the  distance 
of  that  point  of  the  equinoctial  from  the  first 
point  of  Aries,  which  in  an  oblique  sphere  rises 
or  sets,  at  the  same  time  that  the  sun  or  star 
rises  or  sets. 

Ascensional  difference  is  the  difference  betwixt 
right  and  oblique  ascension.  The  sun’s  ascen¬ 
sional  difference  turned  into  time,  is  just  so  much 
as  he  rises  before  or  after  six  o’clock. 

The  celestial  signs  and  constellations  on  the 
surface  of  the  celestial  globe,  are  represented  by 
a  variety  of  human  and  other  figures,  to  which 
the  stars  that  are  either  in  or  near  them,  are  re¬ 
ferred. 

The  several  systems  of  stars,  which  are  applied 
to  those  images,  are  called  constellations.  Twelve 
of  these  are  represented  on  the  ecliptic  circle, 
and  extend  both  northward  and  southward  from 
it.  So  many  of  those  stars  as  fall  within  the 
limits  of  8  degrees  on  both  sides  of  the  ecliptic 
circle,  together  with  such  parts  of  their  images 
as  are  contained  within  the  aforesaid  bounds, 
constitute  a  kind  of  broad  hoop,  belt,  or  girdle, 
which  is  called  the  zodiac . 

342 


OF  THE  GLOBES. 


157 


The  names  and  the  respective  characters  of 
the  twelve  signs  of  the  ecliptic  may  be  learned 
by  inspection  on  the  surface  of  the  broad  paper 
circle,  and  the  constellations  from  the  globe  it¬ 
self. 

The  zodiac  is  represented  by  eight  circles 
parallel  to  the  ecliptic,  on  each  side  thereof ; 
these  circles  are  one  degree  distant  from  each 
other,  so  that  the  whole  breadth  of  the  zodiac  is 
16  degrees. 

Amongst  these  parallels,  the  latitude  of  the 
planets  is  reckoned  ;  and  in  their  apparent  motion 
they  never  exceed  the  limits  of  the  zodiac. 

On  each  side  of  the  zodiac,  as  was  observed, 
other  constellations  are  distinguished  ;  those  on 
the  north  side  are  called  northern,  and  those  on 
the  south  side  of  it,  southern  constellations,. 


OF  THE  PRECESSION  OF  THE  EQUINOXES. 

All  the  stars  which  compose  these  constella- 

A 

lions,  are  supposed  to  increase  their  longitude 
continually ;  upon  which  supposition,  the  whole 
starry  firmament  has  a  slow  motion  from  west 
to  east ;  insomuch  that  the  first  star  in  the  con¬ 
stellation  of  Aries,  which  appeared  in  the  ver¬ 
nal  intersection  of  the  equator  and  ecliptic  in 
the  time  of  Melon  the  Athenian,  upwards  of 

343 


158 


DESCRIPTION  AND  USE 


1 300  years  ago,  is  now  removed  about  30  de¬ 
grees  from  it. 

This  change  of  the  stars  in  longitude,  which 
has  now  become  sufficiently  apparent,  is  owing 
to  a  small  retrograde  motion  of  the  equinoctial 
points,  of  about  50  seconds  in  a  year,  which  is 
occasioned  by  the  attraction  of  the  sun  and 
moon  upon  the  protuberant  matter  about  the 
equator.  The  same  cause  also  occasions  a  small 
deviation  in  the  parallelism  of  the  earth’s  axis, 
by  which  it  is  continually  directed  towards  dif¬ 
ferent  points  in  the  heavens,  and  makes  a  com¬ 
plete  revolution  round  the  ecliptic  in  about 
25,920  years.  The  former  of  these  motions  is 
called  the  precession  of  the  equinoxes ,  the  latter  the 
nutation  of  the  earth' s  axis .  In  consequence  of 
this  shifting  of  the  equinoctial  points,  an  altera¬ 
tion  has  taken  place  in  the  signs  of  the  ecliptic  ; 
those  stars,  which  in  the  infancy  of  astronomy 
were  in  Aries,  being  now  got  into  Taurus,  those 
of  Taurus  into  Gemini,  &c. ;  so  that  the  stars 
which  rose  and  set  at  any  particular  seasons  of 
the  year,  in  the  times  of  Hesiod,  Eudoxus,  and 
Virgil,  will  not  at  present  answer  the  descriptions 
given  of  them  by  those  writers. 

344 


OF  THE  GLOBES. 


159 


PROBLEM  I. 

To  represent  the  motion  of  the  equinoctial  points 
backwards ,  or  in  antecedents ,  upon  the  celestial 
globe ,  elevate  the  north  pole  so  that  it’s  axis  may 
be  perpendicular  to  the  plane  of  the  broad  paper 
circle,  and  the  equator  will  then  be  in  the  same 
plane ;  let  these  represent  the  ecliptic,  and  then 
the  poles  of  the  globe  will  also  represent  those 
of  the  ecliptic  ;  the  ecliptic  line  upon  the  globe 
will  at  the  same  time  represent  the  equator,  in¬ 
clined  in  an  angle  of  23 1  degrees  to  the  broad 
paper  circle,  now  called  the  ecliptic,  and  cutting 
it  in  two  points,  which  are  called  the  equinoctial 
intersections. 

Now  if  you  turn  the  globe  slowly  round  upon 
it’s  axis  f  rom  east  to  west,  while  it  is  in  this  posi¬ 
tion,  these  points  of  intersection  will  move  round 
the  same  way  ;  and  the  inclination  of  the  circle, 
which  in  shewing  this  motion  represents  the 
equinoctial,  will  not  be  altered  by  such  a  revo¬ 
lution  of  the  intersecting  or  equinoctial  points. 
This  motion  is  called  the  precession  of  the  equi¬ 
noxes,  because  it  carries  the  equinoctial  points 
backwards  amongst  the  fixed  stars. 

The  poles  of  the  world  seem  to  describe  a 
circle  from  east  to  west,  round  the  poles  of  the 
ecliptic,  arising  from  the  precession  of  the 

345 


160 


DESCRIPTION  AND  USE 


equinox.  It  is  a  very  slow  motion,  for  the  equi¬ 
noctial  points  take  up  72  years  to  move  one 
degree,  and  therefore  they  are  25,920  years  in 
describing  360  degrees,  or  completing  a  revo¬ 
lution. 

This  motion  of  the  poles  is  easily  represented 
by  the  above  described  position  of  the  globe,  in 
which,  if  the  reader  remembers,  the  broad  paper 
circle  represents  the  ecliptic,  and  the  axis  of  the 
globe  being  perpendicular  thereto,  represents 
the  axis  of  the  ecliptic ;  and  the  two  points, 
where  the  circular  lines  meet,  will  represent  the 
poles  of  the  world,  whence,  as  the  globe  is  slowly 
turned  from  east  to  west,  these  points  will  re¬ 
volve  the  same  way  about  the  poles  of  the  globe, 
which  are  here  supposed  to  represent  the  poles 
of  the  ecliptic.  The  axis  of  the  world  may 
revolve  as  above,  although  its  situation,  with 
respect  to  the  ecliptic,  be  not  altered ;  for  the 
points  here  supposed  to  represent  the  poles  of 
the  world,  will  always  keep  the  same  distance 
from  the  broad  paper  circle,  which  represents 
the  ecliptic  in  this  situation  of  the  globe.* 

From  the  different  degrees  of  brightness  in. 
the  stars,  some  appear  to  be  greater  than  others, 
or  nearer  to  us  ;  on  our  celestial  globe  they  are 
distinguished  into  seven  different  magnitudes. 

*  Rutherforth’s  System  of  Nat.  Philos,  vol.  ii.  p.  730. 


346 


( 161 ) 


OF  THE 


USE  OF  THE  CELESTIAL  GLOBE, 

IN  THE  SOLUTION  OF 

•l  .  •” 

PROBLEMS  RELATIVE  TO  THE  SUN, 

EVERY  thing  that  relates  to  the  sun  is  of 
such  importance  to  man,  that  in  all  things 
he  claims  a  natural  preheminence.  The  sun  is 
at  once  the  most  beautiful  emblem  of  the  Su¬ 
preme  Being,  and,  under  his  influence,  the  fos¬ 
tering  parent  of  worlds ;  being  present  to  them 
by  his  rays,  cheering  them  by  his  countenance, 
cherishing  them  by  his  heat,  adorning  them  at 
each  returning  spring  with  the  gayest  and  rich¬ 
est  attire,  illuminating  them  with  his  light,  and 
feeding  the  lamp  of  life. 

To  the  ancients  he  was  known  under  a  va¬ 
riety  of  names,  each  characteristic  of  his  dif¬ 
ferent  effects  ;  he  was  their  Hercules,  the  great 
deliverer,  the  restorer  of  light  out  of  darkness, 
the  dispenser  of  good,  continually  labouring 
for  the  happiness  of  a  depraved  race.  He  was 
the  Mithra  of  the  Persians,  a  word  derived 
from  love,  or  mercy,  because  the  whole  world 
is  cherished  by  him,  and  feels  as  it  were  the  ef* 
fects  of  his  love. 


X  347 


1 62 


description  and  use 


In  the  sacred  scriptures,  the  original  source 
of  all  emblematical  writings,  our  Lord  is  called 
our  sun,  and  the  sun  of  righteousness ;  and  as 
there  is  but  one  sun  in  the  heavens,  so  there  is 
but  one  true  God,  the  maker  and  redeemer  of 
all  things,  the  light  of  the  understanding,  and 
the  life  of  the  soul. 

As  in  scripture  our  God  is  spoken  of  as  a 
shield  and  buckler,  so  the  sun  is  characterized 
by  this  mark  o,  representing  a  shield  or  buck¬ 
ler,  the  middle  point,  the  umbo,  or  boss ;  be¬ 
cause  it  is  love,  or  life,  which  alone  can  protect 
from  fear  and  death. 

His  celestial  rays,  like  those  of  the  sun,  take 
their  circuit  round  the  earth  ;  there  is  no  cor¬ 
ner  of  it  so  remote  as  to  be  without  the  reach 
of  their  vivifying  and  penetrating  power.  As 
the  material  light  is  always  ready  to  run  it’s 
heavenly  race,  and  daily  issues  forth  with  re¬ 
newed  vigour,  like  an  invincible  champion,  still 
fresh  to  labour ;  so  likewise  did  our  redeeming 
God  rejoice  to  run  his  glorious  race,  he  ex¬ 
celled  in  strength,  and  triumphed,  and  conti¬ 
nues  to  triumph  over  all  the  powers  of  dark¬ 
ness,  and  is  ever  manifesting  himself  as  the  de¬ 
liverer,  the  protetor,  the  friend,  and  father,  of 
the  human  race.* 

*  Horne  on  the  Psalms. 

348 


OF  THE  GLOBES* 


168 


PLOBLEM  II* 

To  rectify  the  celestial  globe . 

To  rectify  the  celestial  globe ,  is  to  put  it  in  that 
position  in  which  it  may  represent  exactly  the  appa - 
rent  motion  of  the  heavens . 

In  different  places,  the  position  will  vary,  and 
that  according  to  the  different  latitude  of  the 
places.  Therefore,  to  rectify  for  any  place,  find 
first,  by  the  terrestrial  globe,  the  latitude  of  that 
place. 

The  latitude  of  the  place  being  found  in  de¬ 
grees,  elevate  the  pole  of  the  celestial  globe  the 
same  number  of  degrees  and  minutes  above  the 
plane  of  the  horizon,  for  this  is  the  name  given 
to  the  broad  paper  circle,  in  the  use  of  the  ce* 
lestial  globe. 

Thus  the  latitude  of  London  being  51 \  de¬ 
grees,  let  the  globe  be  moved  till  the  plane  of 
the  horizon  cuts  the  meridian  in  that  point. 

The  next  rectification  is  for  the  sun’s  place, 
which  may  be  performed  as  directed  in  prob. 
xxix  ;  or  look  for  the  day  of  the  month  close 
under  the  ecliptic  line,  against  which  is  the  sun’s 
place,  place  the  artificial  sun  over  that  point, 
then  bring  the  sun’s  place  to  the  graduated  edge 
of  the  strong  brazen  meridian,  and  set  the  hour 
index  to  the  most  elevated  twelve. 

S49 


164  DESCRIPTION  AND  USE 

Thus  on  the  24th  of  May  the  sun  is  in  31 
degrees  of  Gemini,  and  is  situated  near  the 
Bull’s  eye  and  the  seven  stars,  which  are  not 
then  visible,  on  account  of  his  superior  light. 
If  the  sun  were  on  that  day  to  suffer  a  total 
eclipse,  these  stars  would  then  be  seen  shining 
with  their  accustomed  brightness. 

Lastly,  set  the  meridian  of  the  globe  north 
and  south,  by  the  compass. 

And  the  globe  will  be  rectified,  or  put  into 
a  similar  position,  to  the  concave  surface  of  the 
heavens,  for  the  given  latitude. 


problem  in. 

To  find  the  right  ascension  and  declination  of  the 

sun  for  any  day . 

Bring  the  sun’s  place  in  the  ecliptic  for  the 
given  day  to  the  meridian,  and  the  degree  of 
the  meridian  directly  over  it  is  the  sun’s  declina¬ 
tion  for  that  day  at  noon.  The  point  of  the 
equinoctial  cut  by  the  meridian,  when  the  sun’s 
place  is  under  it,  will  be  the  right  ascension. 

Thus  April  19,  the  sun’s  declination  is  11° 
14’  north,  his  right  ascension  27°  30  .  On  the 
1st  of  December  the  sun’s  declination  is  21°  54' 
south,  right  ascension  247°  50'. 

350 


/ 


OF  THE  GLOBES. 


165 


PROBLEM  IV. 


To  find  the  sun’s  oblique  ascension  and  descension , 
it’s  eastern  and  western  amplitude ,  and  time  of 
rising  and  settings  on  any  given  time ,  in  any 
given  place . 

1.  Rectify  the  globe  for  the  latitude,  the  ze¬ 
nith,  and  the  sun’s  place.  2.  Bring  the  sun’s 
place  to  the  eastern  side  of  the  horizon  ;  then 
the  rnumber  of  degrees  intercepted  between  a 
degree  of  the  equinoctial  at  the  horizon  and  the 
beginning  of  Aries,  is  the  sun’s  oblique  ascen¬ 
sion.  3.  The  number  of  degrees  on  the  hori¬ 
zon  intercepted  between  the  east  point  and  the 
sun’s  place,  is  the  eastern  or  rising  amplitude, 
4.  The  hour  shewn  by  the  index  is  the  time 
of  sun-rising.  5.  Carry  the  sun  to  the  western 
side  of  the  horizon,  and  you  in  the  same  man¬ 
ner  obtain  the  oblique  descension,  western  am¬ 
plitude,  and  time  of  setting.  Thus  at  London, 
May  1, 


oblique  ascension 

18° 

48' 

Eastern  amplitude 

24 

57  N 

Time  of  rising 

4  h 

40  m 

Oblique  descension 

257° 

T 

Western  amplitude 

26 

9 

Time  of  setting 

7  h 

4  m 

351 


‘16*6 


DESCRIPTION  AND  USE 


PROBLEM  V. 

To  find  the  sun’s  meridian  altitude . 

Rectify  the  globe  for  the  latitude,  zenith, 
and  sun’s  place ;  and  when  the  sun’s  place  is  in 
the  meridian,  the  degrees  between  that  point 
and  the  horizon  are  it’s  meridian  altitude.  Thus, 
on  May  17,  at  London,  the  meridian  altitude 
of  the  sun  is  57°  55'. 

PROBLEM  VI. 

To  find  the  length  of  any  day  in  the  year ,  in  any 
latitude ,  not  exceeding  66 1  degrees . 

Elevate  the  celestial  globe  to  the  latitude,  and 
set  the  center  of  the  artificial  sun  to  his  place 
upon  the  ecliptic  line  on  the  globe  for  the  given 
day,  and  bring  it’s  center  to  the  strong  brass 
meridian,  placing  the  horary  index  to  that  XII 
which  is  most  elevated  ;  then  turn  the  globe 
till  the  artificial  sun  cuts  the  eastern  edge  of  the 
horizon,  and  the  horary  index  will  shew  the 
time  of  sun-rising ;  turn  it  to  the  western  side, 
and  you  obtain  the  hour  of  sun-setting. 

The  length  of  the  day  and  night  will  be  ob¬ 
tained  by  doubling  the  time  of  sun-rising  and 
setting,  as  before. 


352 


OF  THE  GLOBES* 


167 


PROBLEM  VIL 

To  find  the  length  of  the  longest  and  shortest 
days  in  any  latitude  that  does  not  exceed  66k  de¬ 
grees . 

Elevate  the  globe  according  to  the  latitude, 
and  place  the  center  of  the  artificial  sun  for  the 
longest  day  upon  the  first  point  of  Cancer,  but 
for  the  shortest  day  upon  the  first  point  of  Ca¬ 
pricorn  ;  then  proceed  as  in  the  last  problem. 

But  if  the  place  hath  south  latitude,  the  sun 
is  in  the  first  point  of  Capricorn  on  their  longest 
day,  and  in  the  first  point  of  Cancer  on  their 
shortest  day. 


PROBLEM  VIII. 

To  find  the  latitude  of  a  place ,  in  which  it’s  long¬ 
est  day  may  be  of  any  given  length  between 
twelve  and  twenty  four  hours . 

Set  the  artificial  sun  to  the  first  point  of  Can¬ 
cer,  bring  its  center  to  the  strong  brass  meri¬ 
dian,  and  set  the  horary  index  to  XII ;  turn  the 
globe  till  it  points  to  half  the  number  of  the 
given  hours  and  minutes ;  then  elevate  or  de¬ 
press  the  pole  till  the  artificial  sun  coincides 
with  the  horizon,  and  that  elevation  of  the  pole 

is  the  latitude  required. 

353 


168 


DESCRIPTION  AND  USE 


PROBLEM  IX. 

To  find  the  time  of  the  sun's  rising  and  settings 
the  length  of  the  dag  and  nighty  on  any  place 
whose  latitude  lies  between  the  polar  circles  ;  and 
also  the  length  of  the  shortest  day  in  any  of  those 
latitudes ,  and  in  what  climate  they  are . 

Rectify  the  globe  to  the  latitude  of  the  given 
place,  and  bring  the  artificial  sun  to  his  place  in 
the  ecliptic  for  the  given  day  of  the  month  ; 
and  then  bring  it’s  center  under  the  strong  brass 
meridian,  and  set  the  horary  index  to  that  XII 
which  is  most  elevated. 

Then  bring  the  center  of  the  artificial  sun  to 
the  eastern  part  of  the  broad  paper  circle, 
which  in  this  case  represents  the  horizon,  and 
the  horary  index  shews  the  time  of  the  sun¬ 
rising;  turn  the  artificial  sun  to  the  western  side, 
and  the  horary  index  will  shew  the  time  of  the 
sun-setting. 

Double  the  time  of  sun-rising  is  the  length 
of  the  night,  and  the  double  of  that  of  sun-set¬ 
ting  is  the  length  of  the  day. 

Thus,  on  the  5th  day  of  June,  the  sun  rises 
at  3  h.  40  min.  and  sets  at  8  h.  20.  min. ;  by 
doubling  each  number  it  will  appear,  that  the 
length  of  this  day  is  16  h.  40.  min.  and  that  of 
the  night  7  h.  20  min. 

354 


OF  THE  GLOBES. 


169 


The  longest  day  at  all  places  in  north  latitude, 
is  when  the  sun  is  in  the  first  point  of  Cancer. 
And, 

The  longest  day  to  those  in  south  latitude,  is 
when  the  sun  is  in  the  first  point  of  Capricorn. 

Wherefore,  the  globe  being  rectified  as  above, 
and  the  artificial  sun  placed  to  the  first  point  of 
Cancer,  and  brought  to  the  eastern  edge  of  the 
broad  paper  circle,  and  the  horary  index  being 
set  to  that  XII  which  is  most  elevated,  on  turn¬ 
ing  the  globe  from  east  to  west,  until  the  arti¬ 
ficial  sun  coincides  with  the  western  edge,  the 
number  of  hours  counted,  which  are  passed  over 
by  the  horary  index,  is  the  length  of  the  longest 
day  ;  their  complement  to  twenty-four  hours 
gives  the  length  of  the  shortest  night. 

If  twelve  hours  be  subtracted  from  the  length 
of  the  longest  day,  and  the  remaining  hours 
doubled,  you  obtain  the  climate  mentioned  by 
ancient  historians;  and  if  you  take  half  the 
climate,  and  add  thereto  twelve  hours,  you 
obtain  the  length  of  the  longest  day  in  that  cli¬ 
mate.  This  holds  good  for  every  climate  be¬ 
tween  the  polar  circles. 

A  climate  is  a  space  upon  the  surface  of 
the  earth,  contained  between  two  parallels  of 
latitude,  so  far  distant  from  each  other,  that 

Y  355 


170 


DESCRIPTION  AND  USE 


the  longest  day  in  one,  differs  half  an  hour  from 
the  longest  day  in  the  other  parallel. 


problem  x. 

The  latitude  of  a  place  being  given  in  one  of  the 
polar  circles ,  ( suppose  the  northern )  to  find 
what  number  of  daps  (of  24  hours  each )  the 
sun  doth  constantly  shine  upon  the  same ,  how 
long  he  is  absent ,  and  also  the  first  and  last  day 
of  his  appearance . 

Having  rectified  the  globe  according  to  the 
latitude,  turn  it  about  until  some  point  in  the 
first  quadrant  of  the  ecliptic  (because  the  latitude 
is  north)  intersects  the  meridian  in  the  north 
point  of  the  horizon ;  and  right  against  that 
point  of  the  ecliptic,  on  the  horizon,  stands  the 
day  of  the  month  when  the  longest  day  begins. 

And  if  the  globe  be  turned  about  till  some 
point  in  the  second  quadrant  of  the  ecliptic  cuts 
the  meridian  in  the  same  point  of  the  horizon,  it 
will  shew  the  sun’s  place  when  the  longest  day 
ends,  whence  the  day  of  the  month  may  be 
found,  as  before ;  then  the  number  of  natural 
days  contained  between  the  times  the  longest 
day  begins  and  ends,  is  the  length  of  the  longest 
day  required. 

Again,  turn  the  globe  about,  until  some 

356 


OF  THE  GLOBES. 


171 


point  in  the  third  quadrant  of  the  ecliptic  cuts 
the  meridian  in  the  south  part  of  the  horizon  ; 
that  point  of  the  ecliptic  will  give  the  time  when 
the  longest  night  begins. 

Lastly,  turn  the  globe  about,  until  some  point 
in  the  fourth  quadrant  of  the  ecliptic  cuts  the 
meridian  in  the  south  point  of  the  horizon ;  and 
that  point  of  the  ecliptic  will  be  the  place  of  the 
sun  when  the  longest  night  ends. 

Or,  the  time  when  the  longest  day  or  night 
begins  being  known,  their  end  may  be  found  by 
counting  the  number  of  days  from  that  time  to 
the  succeeding  solstice ;  then  counting  the  same 
number  of  days  from  the  solstitial  day,  will  give 
the  time  when  it  ends. 


OF  THE  EQUATION  OF  TIME. 


It  is  not  possible,  in  a  treatise  of  this  kind, 
to  enter  into  a  disquisition  of  the  nature  of 
time.  It  is  sufficient  to  observe,  that  if  we 
would  with  exactness  estimate  the  quantity  of 
any  portion  of  infinite  duration,  or  convey  an 
idea  of  the  same  to  others,  we  make  use  of 
such  known  measures  as  have  been  originally 
borrowed  from  the  motions  of  the  heavenly 
bodies.  It  is  true,  none  of  these  motions  are 
exactly  equal  and  uniform,  but  are  subject  to 

357 


172 


DESCRIPTION  AND  USE 


some  small  irregularities,  which,  though  of  no 
consequence  in  the  affairs  of  civil  life,  must  be 
taken  into  the  account  in  astronomical  calcula¬ 
tions.  There  are  other  irregularities  of  more 
importance,  one  of  which  is  in  the  inequality  of 
the  natural  day. 

It  is  a  consideration  that  cannot  be  reflected 
upon  without  surprise,  that  wherever  we  look 
for  commensurabilities  and  equalities  in  nature, 
we  are  always  disappointed.  The  earth  is  spheri¬ 
cal,  but  not  perfectly  so  ;  the  summer  is  une¬ 
qual,  when  compared  with  the  winter  ;  the  eclip¬ 
tic  disagrees  with  the  equator,  and  never  cuts  it 
twice  in  the  same  equinoctial  point.  The  orbit 
of  the  earth  has  an  eccentricity  more  than  double 
in  proportion  to  the  spheroidity  of  it’s  globe  ; 
no  number  of  the  revolutions  of  the  moon  coin¬ 
cides  with  any  number  of  the  revolutions  of  the 
earth  in  it’s  orbit ;  no  two  of  the  planets  measure 
one  another :  and  thus  it  is  wherever  we  turn 
our  thoughts,  so  different  are  the  views  of  the 
Creator  from  our  narrow  conception  of  things ; 
where  we  look  for  commensuration,  we  find 
variety  and  infinity. 

Thus  ancient  astronomers  looked  upon  the 
motion  of  the  sun  to  be  sufficiently  regular  for 
the  mensuration  of  time ;  but,  by  the  accurate 
observations  of  later  astronomers,  it  is  found 

358 


OF  THE  GLOBES. 


173 


that  neither  the  days,  nor  even  the  hours,  as 
measured  by  the  sun’s  apparent  motion,  are  of 
an  equal  length,  on  two  accounts. 

1st,  A  natural  or  solar  day  of  24  hours,  is 
that  space  of  time  the  sun  takes  up  in  passing 
from  any  particular  meridian  to  the  same  again  ; 
but  one  revolution  of  the  earth,  with  respect  to  a 
fixed  star,  is  performed  in  23  hours,  56  minutes, 
4  seconds  ;  therefore  the  unequal  progression  of 
the  earth  through  her  elliptical  orbit,  (as  she 
takes  almost  eight  days  more  to  run  through  the 
northern  half  of  the  ecliptic,  than  she  does  to 
pass  through  the  southern)  is  the  reason  that  the 
length  of  the  day  is  not  exactly  equal  to  the 
time  in  which  the  earth  performs  it’s  rotation 
about  it’s  axis. 

2dly,  From  the  obliquity  of  the  ecliptic  to  the 
equator,  on  which  last  we  measure  time ;  and  as 
equal  portions  of  one  do  not  correspond  to  equal 
portions  of  the  other,  the  apparent  motion  of 
the  sun  would  not  be  uniform ;  or,  in  other 
words,  those  points  of  the  equator  which  come 
to  the'  meridian,  with  the  place  of  the  sun  on 
different  days,  would  not  be  at  equal  distances 
from  each  other. 


359 


1 74 


DESCRIPTION  AND  USE 


PROBLEM  XI. 

To  illustrate ,  by  the  globe ,  much  of  the  equation 

gJ  time  as  is  in  consequence  of  the  sun’s  apparent 
motion  in  the  ecliptic . 

Bring  every  tenth  degree  of  the  ecliptic  to  the 
graduated  side  of  the  strong  brass  meridian,  and 
you  will  find  that  each  tenth  degree  on  the  equa¬ 
tor  will  not  come  thither  with  it ;  but  in  the 
following  order  from  t  to  qs,  every  tenth  de¬ 
gree  of  the  ecliptic  comes  sooner  to  the  strong 
brass  meridian  than  their  corresponding  tenths 
on  the  equator ;  those  in  the  second  quadrant  of 
the  ecliptic,  from  25  to  ^=,  come  later,  from  =*= 
to  vj  sooner,  and  from  v?  to  Aries  later,  whilst 
those  at  the  beginning  of  each  quadrant  come  to 
the  meridian  at  the  same  time  ;  therefore  the  sun 
and  clock  would  be  equal  at  these  four  times,  if 
the  sun  was  not  longer  in  passing  through  one 
half  of  the  ecliptic  than  the  other,  and  the  two 
inequalities  joined  together,  compose  that  diffe¬ 
rence  which  is  called  the  equation  of  time. 

'  These  causes  are  independent  of  each  other, 
sometimes  they  agree,  and  at  other  times  are 
contrary  to  one  another. 

The  inequality  of  the  natural  day  is  the  cause 
that  clocks  or  watches  are  sometimes  before, 
sometimes  behind  the  sun. 

360 


OF  THE  GLOBES. 


175 


A  good  and  well  regulated  clock  goes  uniformly 
on  throughout  the  year,  so  as  to  mark  the  equal 
hours  of  a  natural  day,  of  a  mean  length  ;  a  sun¬ 
dial  marks  the  hours  of  every  day  in  such  a 
manner,  that  every  hour  is  a  24th  part  of  the 
time  between  the  noon  of  that  day,  and  the  noon 
of  the  day  immediately  following.  The  time 
measured  by  a  clock  is  called  equal  or  true 
time,  that  measured  by  the  sun-dial  apparent 
time. 

THE  USE  OF  THE  CELESTIAL  GLOBE,  IN  PROB¬ 
LEMS  RELATIVE  TO  THE  FIXED  STARS. 

The  use  of  the  celestial  globe  is  in  no  instance 
more  conspicuous,  than  in  the  problems  con¬ 
cerning  the  fixed  stars.  Among  many  other 
advantages,  it  will,  if  joined  with  observations 
on  the  stars  themselves,  render  the  practice  and 
theory  of  other  problems  easy  and  clear  to  the 
pupil,  and  vastly  facilitate  his  progress  in  astro¬ 
nomical  knowledge. 

The  heavens  are  as  much  studded  over  with 
stars  in  the  day,  as  in  the  night ;  only  they 
are  then  rendered  invisible  to  us  by  the  bright¬ 
ness  of  the  solar  rays.  But  when  this  glorious 
luminary  descends  below  the  horizon,  they  be¬ 
gin  gradually  to  appear ;  when  the  sun  is  about 
twelve  degrees  below  the  horizon,  stars  of  the 
first  magnitude  become  visible  ;  when  he  is 

361 


176  DESCRIPTION  AND  USE 

thirteen  degrees,  those  of  the  second  are  seen ; 
when  fourteen  degrees,  those  of  the  third  mag¬ 
nitude  appear ;  when  fifteen  degrees,  those  of 
the  fourth  present  themselves  to  view  ;  when  he 
is  descended  about  eighteen  degrees,  the  stars 
of  the  fifth  and  sixth  magnitude,  and  those  that 
are  still  smaller,  become  conspicuous,  and  the 
azure  arch  sparkles  with  all  it’s  glory. 

v 

PROBLEM  XII.  1 

To  find  the  right  ascension  and  declination  of  any 

given  star . 

Bring  the  given  star  to  the  meridian,  and  the 
degree  under  which  it  lies  is  it’s  declination ;  and 
the  point  in  which  the  meridian  intersects  the 
equinoctial  is  it’s  right  ascension.  Thus  the  right 
ascension  of  Sirius  is  99°,  it’s  declination  16°  2 5' 
south;  the  right  ascension  of  Arcturus  is  211° 
32'.  it’s  declination  20°  20'  north. 

The  declination  is  used  to  find  the  latitude  of 
places ;  the  right  ascension  is  used  to  find  the 
time  at  which  a  star  or  planet  comes  to  the  me¬ 
ridian  ;  to  find  at  any  given  time  how  long  it 
will  be  before  any  celestial  body  comes  to  the 
meridian ;  to  determine  in  what  order  those 
bodies  pass  the  meridian ;  and  to  make  a  cata¬ 
logue  of  the  fixed  stars. 

.362 


OF  THE  GLOBES, 


177 


PROBLEM  XIII. 

To  find  the  latitude  and  longitude  of  a  given 

star . 

Bring  the  pole  of  the  ecliptic  to  the  meri¬ 
dian,  over  which  fix  the  quadrant  of  altitude, 
and,  holding  the  globe  very  steady,  move  the 
quadrant  to  lie  over  the  given  star,  and  the  de¬ 
gree  on  the  quadrant  cut  by  the  star,  is  it’s  la¬ 
titude  ;  the  degree  of  the  ecliptic  cut  at  the 
same  time  by  the  quadrant,  is  the  longitude  of 
the  star. 

Thus  the  latitude  of  Arcturus  is  30°  30' ; 
it’s  longitude  20°  20  of  Libra  :  the  latitude  of 
Capella  is  22°  22'  north;  it’s  longitude  18  8'  of 
Gemini, 

The  latitude  and  longitude  of  stars  is  used 
to  fix  precisely  their  place  on  the  globe,  to  re¬ 
fer  planets  and  comets  to  the  stars,  and,  lastly, 
to  determine  whether  they  have  any  motion, 
whether  any  stars  vanish,  or  new  ones  appear, 

PROBLEM  xiv„ 

The  right  ascension  and  declination  of  a  star  being 
given ,  to  find  it’s  place  on  the  globe . 

Turn  the  globe  till  the  meridian  cuts  the 
equinoctial  in  the  degree  of  right  ascension. 

Z  363 


\ 


178  DESCRIPTION  AND  USE 

Thus  for  example,  suppose  the  right  ascension 
of  Aldebaran  to  be  65°  30',  and  it’s  declination 
to  be  16°  north,  then  turn  the  globe  about  till 
the  meridian  cuts  the  equinoctial  in  65°  30', 
and  under  the  16°  of  the  meridian,  on  the  nor¬ 
thern  part,  you  will  observe  the  star  Aldebaran* 
or  the  bull’s  eye. 


problem  xv. 


To  find  at  what  hour  any  known  star  passes  the 
meridian ,  at  any  given  day. 

Find  the  sun’s  place  for  that  day  in  the 
ecliptic,  and  bring  it  to  the  strong  brass  meri¬ 
dian,  set  the  horary  index  to  XII  o’clock,  then 
turn  the  globe  till  the  star  comes  to  the  meri¬ 
dian,  and  the  index  will  mark  the  time.  Thus 
on  the  15th  of  August,  Lyra  comes  to  the  me¬ 
ridian  at  45  min.  past  VIII  in  the  evening.  On 
the  14th  of  September  the  brightest  of  the 
Pleiades  will  be  on  the  meridian  at  IV  in  the 
morning. 

This  problem  is  useful  for  directing  when 
to  look  for  any  star  on  the  meridian,  in  order  to 
find  the  latitude  of  a  place,  to  adjust  a  clock, 
&c. 


364 


OF  THE  GLOBES, 


17^ 


PROBLEM  XVI. 

To  find  on  what  day  a  given  star  will  come  to  the 
meridian  y  at  any  given  hour . 

Bring  the  given  star  to  the  meridian,  and 
set  the  index  to  the  proposed  hour ;  then  turn 
the  globe  till  the  index  points  to  XII  at  noon, 
and  observe  the  degree  of  the  ecliptic  then  at 
the  meridian ;  this  is  the  sun’s  place,  the  day 
answering  to  which  may  be  found  on  the  calen¬ 
dar  of  the  broad  paper  circle. 

By  knowing  whether  the  hour  be  in  the  morn¬ 
ing  or  afternoon,  it  will  be  easy  to  perceive 
which  way  to  turn  the  globe,  that  the  proper 
XII  may  be  pointed  to ;  the  globe  must  be  turn¬ 
ed  towards  the  west,  if  the  given  hour  be  in  the 
morning,  towards  the  east  if  it  be  afternoon. 

Thus  Arcturus  will  be  on  the  meridian  at  III 
in  the  morning  on  March  the  5th,  and  Cor  Le» 
onis  at  VIII  in  the  evening  on  April  the  21st. 

PROBLEM  XVII. 

To  represent  the  face  of  the  heavens  on  the  globe  for 
a  given  hour  on  any  day  of  the  year ,  and  learn 
to  distinguish  the  visible  fixed  stars . 

Rectify  the  globe  to  the  given  latitude  oi 
the  place  and  day  of  the  month,  setting  it  due 

365 


180 


DESCRIPTION  AND  USE 


north  and  south  by  the  needle  ;  then  turn  the 
globe  on  it’s  axis  till  the  index  points  to  the  given 
hour  of  the  night  ;  then  all  the  upper  hemis¬ 
phere  of  the  globe  will  represent  the  visible  face 
of  the  heavens  for  that  time,  by  which  it  will 
be  easily  seen  what  constellations  and  stars  of 
note  are  then  above  our  horizon,  and  what  po¬ 
sition  they  have  with  respect  to  the  points  of  the 
compass.  In  this  case,  supposing  the  eye  was 
placed  in  the  center  of  the  globe,  and  holes  were 
pierced  through  the  centers  of  the  stars  on  it’s 
surface,  the  eye  would  perceive  through  those 
holes  the  various  corresponding  stars  in  the  fir¬ 
mament  ;  and  hence  it  would  be  easy  to  know 
the  various  constellations  at  sight,  and  to  be 
able  to  call  all  the  stars  by  their  names. 

Observe  some  star  that  you  know,  as  one  of 
the  pointers  in  the  Great  Bear,  or  Sirius  ;  find 
the  same  on  the  globe,  and  take  notice  of  the 
position  of  the  contiguous  stars  in  the  same  or 
an  adjoining  constellation ;  direct  your  sight  to 
the  heavens,  and  you  will  see  those  stars  in  the 
same  situation.  Thus  you  may  proceed  from  one 
constellation  to  another,  till  you  are  acquainted 
with  most  of  the  principal  stars. 

“  For  example :  the  situation  of  the  stars  at 
London  on  the  9th  of  February,  at  2  min.  past 
IX.  in  the  evening,  is  as  follows. 

“  Sirius,  or  the  Dog-star,  is  on  the  meridian, 

366 


OF  THE  GLOBES. 


181 


it’s  altitude  22°:  Procyon,  or  the  little  Dog-star, 
16°  towards  the  east,  it’s  altitude  43 i  :  about  24° 
above  this  last,  and  something  more  towards 
the  east,  are  the  twins,  Castor  and  Pollux  :  S.o  5° 
E.  and  35°  in  height,  is  the  bright  star  Regulus, 
or  Cor  Leonis :  exactly  in  the  east  and  22°  high, 
is  the  star  Deneb  Alased  in  the  Lion’s  tail  :  30° 
from  the  east  towards  the  north  Arcturus  is 
about  3  above  the  horizon  :  directly  over  Arc¬ 
turus,  and  31°  above  the  horizon,  is  Cor  Caroli: 
in  the  north-east  are  the  stars  in  the  extremity 

j 

of  the  Great  Bear’s  tail,  Aleath  the  first  star  in 
the  tail,  and  Dubhe  the  northernmost  pointer  in 
the  same  constellation  ;  the  altitude  of  the  first 
of  these  is  30! ,  that  of  the  second  41°,  and  that 
of  the  third  56°. 

cc  Reckoning  westward,  we  see  the  beauti¬ 
ful  constellation  Orion ;  the  middle  star  of  the 
three  in  his  belt,  is  S.  20°  W.  it’s  altitude  35° : 
nine  degrees  below  the  belt,  and  a  little  more 
to  the  west,  is  Rigel  the  bright  star  in  his  heel : 
above  his  belt  in  a  strait  line  drawn  from  Rigel 
between  the  middle  and  most  northward  in  his 
belt,  and  9°  above  it,  is  the  bright  star  in  his 
shoulder  :  S.  49°  W.  and  4 51  above  the  horizon, 
is  Aldebaran  the  southern  eye  of  the  Bull :  a 
little  to  the  west  of  Aldebaran,  are  the  Hyades : 
the  same  altitude,  and  about  S.  70°  W,  are  the 
Pleiades  :  in  the  W.  by  S.  point  is  Capella  in 
Auriga,  it’s  altitude  73° :  in  the  north-west,  and 

367 


182 


DESCRIPTION  AND  USE 


about  42°  high,  is  the  constellation  Cassiopeia : 
and  almost  in  the  north,  near  the  horizon,  is  the 
constellation  Cygnus.”* 

PROBLEM  XVIII. 

l  o  trace  the  circles  of  the  sphere  in  the  starry  fir¬ 
mament . 

I  shall  solve  this  problem  for  the  time  of  the 
autumnal  equinox  ;  because  that  intersection  of 
the  equator  and  ecliptic  will  be  directly  under  the 
depressed  part  of  the  meridian  about  midnight ; 
and  then  the  opposite  intersection  will  be  ele¬ 
vated  above  the  horizon  ;  and  also  because  our 
first  meridian  upon  the  terrestrial  globe  passing 
through  London,  and  the  first  point  of  Aries, 
when  both  globes  are  rectified  to  the  latitude  of 
London,  and  to  the  sun’s  place,  and  the  first 
point  of  Aries  is  brought  under  the  graduated 
side  of  each  of  their  meridians,  we  shall  have 
the  corresponding  face  of  the  heavens  and  the 
earth  represented,  as  they  are  with  respect  to 
each  other  at  that  time,  and  the  principal  circles 
of  each  sphere  will  correspond  with  each  other. 

The  horizon  is  then  distinguished,  if  we  be¬ 
gin  from  the  north,  and  count  westward,  by  the 
following  constellations  ;  the  hounds  and  waist 
of  Bootes,  the  northern  crown,  the  head  of 


*  ISrar.sby’s  Use  of  the  Globes. 
868 


OF  THE  GLOBES. 


183 


Hercules,  the  shoulders  of  Serpent arius,  and 
Sobieski’s  shield;  it  passes  a  little  below  the  feet 
of  Antinous,  and  through  those  of  Capricorn, 
through  the  Sculptor’s  frame,  Eridanus,  the  star 
Rigel  in  Orion’s  foot,  the  head  of  Monoceros, 
the  Crab,  the  head  of  the  Little  Lion,  and  low¬ 
er  part  of  the  Great  bear. 

The  meridian  is  then  represented  by  the  equi¬ 
noctial  colure,  which  passes  through  the  star 
marked  $  in  the  tail  of  the  Little  Bear,  under 
the  north  pole,  the  pole  star,  one  of  the  stars  in 
the  back  of  Cassiopeia’s  chair  marked  /?,  the 
head  of  Andromeda,  the  bright  (star  in  the  wing 
of  Pegasus  marked  y,  and  the  extremity  of  the 
tail  of  the  whale. 

That  part  of  the  equator  which  is  then  above 
the  horizon,  is  distinguished  on  the  western  side 
by  the  northern  part  of  Sobieski’s  shield,  the 
shoulder  of  Antinous,  the  head  and  vessel  of 
Aquarius,  the  belly  of  the  western  fish  in  Pisces; 
it  passes  through  the  head  of  the  Whale,  and  a 
bright  star  marked  2  in  the  corner  of  his  mouth, 
and  thence  through  the  star  marked  §  in  the 
belt  of  Orion,  at  that  time  near  the  eastern  side 
of  the  horizon. 

That  half  of  the  ecliptic  which  is  then  above 
the  horizon,  if  we  begin  from  the  western  side, 
presents  to  our  view'  Capricornus,  Aquarius, 
Pisces,  Aries,  Taurus,  Gemini,  and  a  part  of 
the  constellation  Cancer. 

369 


184 


description  and  use 


The  solstitial  coiure,  from  the  western  side, 
passes  through  Cerberus,  and  the  hand  of  Her¬ 
cules,  thence  by  the  western  side  of  the  constel¬ 
lation  Lyra,  and  through  the  Dragon’s  head 
and  body,  through  the  pole  point  under  the 
polar  star,  to  the  east  of  Auriga,  through  the 
star  marked  *>  in  the  foot  of  Castor,  and  through 
the  hand  and  elbow  of  Orion. 

The  northern  polar  circle,  from  that  part  of 
the  meridian  under  the  elevated  pole,  advancing 
towards  the  west,  passes  through  the  shoulder 
of  the  Great  Bear,  thence  a  little  to  the  north 
of  the  star  marked  «  in  the  Dragon’s  tail,  the 
great  knot  of  the  dragon,  the  middle  of  the 
body  of  Cepheus,  the  northern  part  of  Cassiopeia, 
and  base  of  her  throne,  through  Cameloparda- 
lus,  and  the  head  of  the  Great  Bear. 

The  tropic  of  Cancer,  from  the  western 
edge  of  the  horizon,  passes  under  the  arm  of 
Hercules,  under  the  Vulture,  through  the  Goose 
and  Fox,  which  is  under  the  beak  and  wing  of 
the  Swan,  under  the  star  called  Sheat,  marked  (2 
in  Pegasus,  under  the  head  of  Andromeda,  and 
through  the  star  marked  <*>  in  the  fish  of  the  con¬ 
stellation  Pisces,  above  the  bright  star  in  the 
head  of  the  Ram  marked  <*,  through  the  Pleiades, 
between  the  horns  of  the  Bull,  and  through  a 

group  of  stars  at  the  foot  of  Castor,  thence 
above  a  star  marked  $,  between  Castor  and  Pol¬ 
lux,  and  so  through  a  part  of  the  constellation 

370 


OF  THE  GLOBES* 


185 


Cancer,  where  it  disappears  by  passing  under  the 
eastern  part  of  the  horizon. 

The  tropic  of  Capricorn,  from  the  western 
side  of  the  horizon,  passes  through  the  belly,  and 
under  the  tail  of  Capricorn,  thence  under  Aqua* 
rius,  through  a  star  in  Eridanus  marked  c,  thence 
under  the  belly  of  the  Whale,  through  the  base 
of  the  chemical  Furnace,  whence  it  goes  under 
the  Hare  at  the  feet  of  Orion,  being  there  depres¬ 
sed  under  the  horizon. 

The  southern  polar  circle  is  invisible  to  the 
inhabitants  of  London,  by  being  under  our  ho¬ 
rizon. 

Arctic  and  antarctic  circles ,  or  circles  of  -perpetual 
apparition  and  occupation* 

The  largest  parallel  of  latitude  on  the  terres¬ 
trial  globe,  as  well  as  the  largest  circle  of  decli¬ 
nation  on  the  celestial,  that  appears  entire  above 
the  horizon  of  any  place  in  north  latitude,  was 
called  by  the  ancients  the  arctic  circle,  or  circle 
of  perpetual  apparition. 

Between  the  arctic  circle  and  the  north  pole 
in  the  celestial  sphere,  are  contained  all  those 
stars  which  never  set  at  that  place,  and  seem  to 
us,  by  the  rotative  motion  of  the  earth,  to  be 
perpetually  carried  round  above  our  horizon, 
the  circles  parallel  to  the  equator. 

The  largest  parallel  of  latitude  on  the  ter- 

A  a  371 


186 


description  and  use 


restrial,  and  the  largest  parallel  of  declination 
on  the  celestial  globe,  which  is  entirely  hid  be¬ 
low  the  horizon  of  any  place,  was  by  the  an¬ 
cients  called  the  antarctic  circle,  or  circle  of 
perpetual  occultation. 

This  circle  includes  all  the  stars  which  never 
rise  in  that  place  to  an  inhabitant  of  the  nor¬ 
thern  hemisphere,  but  are  perpetually  below  the 
horizon* 

All  arctic  circles  touch  their  horizons  in  the 
north  point,  and  all  antarctic  circles  touch  their 
horizons  in  the  south  point ;  which  point,  in  the 
terrestrial  and  celestial  spheres,  is  the  intersec¬ 
tion  of  the  meridian  and  horizon. 

If  the  elevation  of  the  pole  be  45  degrees, 
the  most  elevated  part  either  of  the  arctic  or 
antarctic  circle  will  be  in  the  zenith  of  the 
place. 

If  the  pole’s  elevation  be  less  than  45  de¬ 
grees,  the  zenith  point  of  those  places  will  fall 
without  it’s  arctic  or  antarctic  circle ;  if  greater, 
it  will  fall  within. 

Therefore,  the  nearer  any  place  is  to  the 
equator,  the  less  will  it’s  arctic  and  antarctic 
circles  be ;  and  on  the  contrary,  the  farther  any 
place  is  from  the  equator,  the  greater  they  are. 
So  that. 

At  the  poles,  the  equator  may  be  consi¬ 
dered  as  both  an  arctic  and  antarctic  circle, 

372 


OF  THE  GLOBES®  >  187 

because  it5s  plane  is  coincident  with  that  of  the 
horizon. 

But  at  the  equator  (that  is,  in  a  right  sphere) 
there  is  neither  arctic  nor  antarctic  circle® 

They  who  live  under  the  northern  polar  cir¬ 
cle,  have  the  tropic  of  Cancer  for  their  arc¬ 
tic,  and  that  of  Capricorn  for  their  antarctic 
circle. 

And  they  who  live  on  either  tropic,  have  one 
of  the  polar  circles  for  their  arctic,  and  the  other 
for  their  antarctic  circle. 

Hence,  whether  these  circles  fall  within  or 
without  the  tropics,  their  distance  from  the  ze¬ 
nith  of  any  place  is  ever  equal  to  the  difference 
between  the  pole's  elevation,  and  that  of  the 
equator,  above  the  horizon  of  that  place. 

From  what  has  been  said,  it  is  plain  there 
may  be  as  many  arctic  and  antarctic  circles,  as 
there  are  individual  points  upon  any  one  meri¬ 
dian,  between  the  north  and  south  poles  of  the 
earth. 

Many  authors  have  mistaken  these  mutable 
circles,  and  have  given  their  names  to  the  im¬ 
mutable  polar  circles,  which  last  are  arctic  and 
antarctic  circles,  in  one  particular  case  only,  as 
has  been  shewn. 


373 


188 


DESCRIPTION  AND  USE 


PROBLEM  XIX. 

To  find  the  circle ,  or  parallel  of  perpetual  appa¬ 
rition ,  or  occulation  of  a  fixed  star ,  in  a  given 
latitude . 

By  rectifying  the  globe  to  the  latitude  of  the 
place,  and  turning  it  round  on  it’s  axis,  it  will 
be  immediately  evident,  that  the  circle  of  perpe¬ 
tual  apparition  is  that  parallel  of  declination 
which  is  equal  to  the  complement  of  the  given 
latitude  northward ;  and  for  the  perpetual  oc~ 
cultation,  it  is  the  same  parallel  southward;  that 
is  to  say,  in  other  words,  all  those  stars,  whose 
declinations  exceed  the  co-latitude,  will  always 
be  visible,  or  above  the  horizon ;  and  all  those 
in  the  opposite  hemisphere,  whose  declination 
exceeds  the  co-latitude,  never  rise  above  the 
horizon. 

For  instance  ;  in  the  latitude  of  London  51 
deg.  30  min.  whose  co-latitude  is  38  deg.  30 
min.  gives  the  parallels  desired  ;  for  all  those 
stars  which  are  within  the  circle,  towards  the 
north  pole,  never  descend  below  our  horizon ; 
and  all  those  stars  which  are  within  the  same 
circle,  about  the  south  pole,  can  never  be  seen 
in  the  latitude  of  London,  as  they  never  ascend 
above  it’s  horizon. 


374 


OF  THE  GLOBES. 


189 


Or  PROBLEMS  RELATING  TO  THE  AZIMUTH,  See. 

OF  THE  SUN  AND  STARS. 

PROBLEM  XX. 

The  latitude  of  the  place  and  the  sun’s  place  being 
given ,  to  find  the  sun’s  amplitude. 

That  degree  from  east  or  west  in  the  horizon , 
wherein  any  object  rises  or  sets9  is  called  the  am¬ 
plitude . 

Rectify  the  globe,  and  bring  the  sun’s  place 
to  the  eastern  side  of  the  meridian,  and  the  arch 
of  the  horizon  intercepted  between  that  point 
and  the  eastern  point,  will  be  the  sun’s  ampli¬ 
tude  at  rising. 

If  the  same  point  be  brought  to  the  western 
side  of  the  horizon,  the  arch  of  the  horizon  in¬ 
tercepted  between  that  point  and  the  western 
point,  will  be  the  sun’s  amplitude  at  setting. 

Thus  on  the  24th  of  May  the  sun  rises  at 
four,  writh  36  degrees  of  eastern  amplitude,  that 
is,  36  degrees  from  the  east  towards  the  north, 
and  sets  at  eight,  with  36  degrees  of  western  am¬ 
plitude. 

The  amplitude  of  the  sun  at  rising  and  set¬ 
ting  increases  with  the  latitude  of  the  place : 
and  in  very  high  northern  latitudes,  the  sun 
scarce  sets  before  he  rises  again.  Homer  had 

375 


190 


DESCRIPTION  AND  USE 


heard  something  of  this,  though  it  is  not  true  of 
the  Lsestrygones,  to  whom  he  applies  it. 


Six  days  and  nights  a  doubtful  course  we  steer; 
The  next,  proud  Lamos*  lofty  towers  appear, 
And  Lsestygonia’s  gates  arise  distinct  in  air. 

The  shepherd  quitting  here  at  night  the  plain, 
Calls,  to  succeed  his  cares,  the  watchful  swain. 
But  he  that  scorns  the  chains  of  sleep  to  wear, 
And  adds  the  herdsman’s  to  the  shepherd’s  care, 
So  near  the  pastures,  and  so  short  the  way, 

His  double  toils  may  claim  a  double  pay, 

And  join  the  labours  of  the  ngiht  and  day. 


PROBLEM  XXI. 


To  find  the  sun’s  altitude  at  any  given  time  of  the 

day . 

Set  the  center  of  the  artificial  sun  to  his 
place  in  the  ecliptic  upon  the  globe,  and  rec¬ 
tify  it  to  the  latitude  and  zenith  j  bring  the  cen¬ 
ter  of  the  artificial  sun  under  the  strong  brass 
meridian,  and  set  the  hour  index  to  that  XII 
which  is  most,  elevated  ;  turn  the  globe  to  the 
given  hour,  and  move  the  graduated  edge  of  the 
quadrant  to  the  center  of  the  artificial  sun ;  and 
that  degree  on  the  quadrant,  which  is  cut  by  the 
sun’s  center,  is  the  sun’s  height  at  that  time. 

The  artificial  sun  being  brought  under  the 
strong  brass  meridian,  and  the  quadrant  laid 

376 


OF  THE  GLOBES. 


191 


upon  it’s  center,  will  shew  it’s  meridian ,  or  great¬ 
est  altitude ,  for  that  day. 

If  the  sun  be  in  the  equator,  his  greatest  or 
meridian  altitude  is  equal  to  the  elevation  of 

the  equator,  which  is  always  equal  to  the  co-la- 

» 

titude  of  the  place. 

Thus  on  the  24th  of  May,  at  nine  o’clock, 
the  sun  has  44  deg.  altitude,  and  at  six  in  the 
afternoon  20  deg. 

% 

k  <  j 

OF  THE  AZIMUTHAL  OR  VERTICAL  CIRCLES. 

The  vertical  point,  that  is,  the  uppermost 
point  of  the  celestial  globe,  represents  a  point 
in  the  heavens,  directly  over  our  heads,  which 
is  called  our  zenith. 

From  this  point  circular  lines  may  be  con¬ 
ceived  crossing  the  horizon  at  right  angles. 

These  are  called  azimuth ,  or  vertical  circles.. 
That  one  which  crosses  the  horizon  at  10  deg. 
distance  from  the  meridian  on  either  side,  is 
called  an  azimuth  circle  of  10  deg.  ;  that 
which  crosses  at  20,  is  called  an  azimuth  of 
20  deg. 

The  azimuth  of  90  deg.  is  called  the  prime 
vertical :  it  crosses  the  horizon  at  the  eastern 
and  western  points.  *  v 

Any  azimuth  circle  may  be  represented  by 
the  graduated  edge  of  the  brass  quadrant  of 

377 


192 


description  and  use 


altitude,  when  the  center  upon  which  it  turns 
is  screwed  to  that  point  of  the  strong  brass  me¬ 
ridian  which  answers  to  the  latitude  of  the 
place,  and  the  place  is  brought  into  the  zenith. 

If  the  said  graduated  edge  should  lie  over 
the  sun’s  center  or  place,  at  any  given  time, 
it  will  represent  the  sun’s  azimuth  at  that 
time. 

If  the  graduated  edge  be  fixed  at  any  point, 
so  as  to  represent  any  particular  azimuth,  and 
the  sun’s  place  be  brought  there,  the  horary  in¬ 
dex  will  shew  at  what  time  of  that  day  the  sun 
will  be  in  that  particular  azimuth. 

Here  it  may  be  observed,  that  the  amplitude 
and  azimuth  are  much  the  same. 

The  amplitude  shewing  the  bearing  of  any  ob¬ 
ject  when  it  rises  or  sets ,  from  the  east  and  west 
points  of  the  horizon. 

The  azimuth  the  bearing  of  any  object  when 
it  is  above  the  horizon ,  either  from  the  north  or 
south  points  thereof.  These  descriptions  and 
illustrations  being  understood,  we  may  proceed 

to 


378 


OF  THE  GLOBES, 


195 


PROBLEM  XXII. 

To  find  at  what  time  the  sun  is  due  east ,  the  day 
and  the  latitude  being  given . 

Rectify  the  globe ;  then  if  the  latitude  and 
declination  are  of  one  kind,  bring  the  quadrant, 
of  altitude  to  the  eastern  point  of  the  horizon., 
and  the  sun’s  place  to  the  edge  of  the  quadrant, 
and  the  index  will  shew  the  hour. 

If  the  latitude  and  declination  are  of  different 
kinds,  bring  the  quadrant  to  the  western  point 
of  the  horizon,  and  the  point  in  the  ecliptic  op¬ 
posite  to  the  sun’s  place  to  the  edge  of  the  quad- 
rant,  and  then  the  index  will  shew  the  hour. 

You  wili  easily  comprehend  the  reason  of  the 
foregoing  distinction,  because  when  the  sun  is  in 
the  equinoctial,  it  rises  due  east ;  but  when  it  is  in 
that  part  of  the  ecliptic  which  is  toVards  the  ele¬ 
vated  pole,  it  rises  before  it  is  in  the  eastern  verti¬ 
cal  circle,  and  is  therefore  at  that  time  above  the 
horizon:  whereas  when  it  is  in  the  other  part  of 
the  ecliptic,  it  passes  the  eastern  prime  vertical 
before  it  rises,  that  is  below  the  horizon;  whence 
it  is  evident,  that  the  opposite  point  of  the  ecliptic 
must  then  be  in  the  west,  and  above  the  horizon. 
The  sun  is  due  east  at  Loudon  at  7  h.  6  min.  on 

Rb  379 


194 


description  and  use 


the  18th  of  May.  The  second  of  August,  at 
Cape  Horn,  the  sun  is  due  east  at  5  h.  10  min. 

#  .  /  1  i 

PROBLEM  XXIII.  ' 

•» 

To  find  the  rising ,  setting ,  culminating  of  a 

star ,  /7\f  continuance  above  the  horizon ,  #^<7  /Vr 
oblique  ascension  and  descension ,  /V’r 

eastern  and  western  amplitude , for  any  given  day 

X 

place* 

,  •  i  » 

1.  Rectify  the  globe  to  the  latitude  and  ze¬ 
nith,  bring  the  sun’s  place  for  the  day  to  the 
meridian,  and  set  the  hour  index  to  XII.  2.  Bring 
the  star  to  the  eastern  side  of  the  horizon,  and 
it’s  eastern  amplitude,  oblique  ascension,  and 
time  of  rising,  will  be  found  as  taught  of  the 
sun.  3.  Carry  the  star  to  the  western  side  of 
the  horizon  ;  and  in  the  same  manner  it’s  west¬ 
ern  amplitude,  oblique  descension,  and  time  of 
setting,  will  be  found.  4.  The  time  of  rising, 
subtracted  from  that  of  setting,  leaves  the  con¬ 
tinuance  of  the  star  above  the  horizon.  5.  This 
remainder,  subtracted  from  24  hours,  gives  the 
time  of  it’s  continuance  below  the  horizon, 
6.  The  hour  to  which  the  index  points,  when 
the  star  comes  to  the  meridian,  is  the  time  of  it’s 
culminating  or  being  on  the  meridian. 

Let  the  given  day  be  March  14,  the  place 

380 


9. 

OF  THE  GLOBES.  195 

London,  the  star  Sirius  ;  by  working  the  prob* 


lem,  you  will  find 

It  rises  at 

2  h. 

24  min.  afternoon. 

Culminates 

6 

57 

V 

Sets  at  - 

11 

50 

Is  above  the  horizon 

9 

6 

It’s  oblique  ascension  and  descension  are  120° 
47,  and  77°  1 5  ;  it’s  amplitude  27°,  southward. 


PROBLEM  XXIV. 

V  .  t  *  * 

I 

The  latitude ,  the  altitude  of  the  sun  by  day ,  or  of 
j# .star  by  night ,  being  given ,  find  the  hour  of 
the  day ,  the  surfs  or  starfs  azimuth . 

Rectify  the  globe  for  the  latitude,  the  zenith, 
and  the  sun’s  place,  turn  the  globe  and  the  quad¬ 
rant  of  altitude,  so  that  the  sun’s  place,  or  the 
given  star,  may  cut  the  given  degree  of  altitude, 
the  index  will  shew  the  hour,  and  the  quadrant 
will  be  the  azimuth  in  the  horizon. 

Thus  on  the  21st  of  August,  at  London,  when 
the  sun’s  altitude  is  36°  in  the  forenoon,  the  hour  - 
is  IX,  and  the  azimuth  58 0  from  the  south. 

At  Boston,  December  8th,  when  Rigel  had  15 
of  altitude,  the  hour  was  VIII,  the  azimuth  S,  E. 
by  E.  7°. 


381 


196 


DESCRIPTION  AND  USE 


♦ 

\ 

PROBLEM  XXV. 

The  latitude  and  hour  of  the  day  being  given ,  to 
find  the  altitude  and  azimuth  of  the  fsun,  or  of 
a  star . 

Rectify  the  globe  for  the  latitude,  the  zenith, 
and  the  sun’s  place,  then  the  number  of  degrees 
contained  betwixt  the  sun’s  place  and  the  vertex 
is  the  sun’s  meridional  zenith  distance ;  the 
complement  of  which  to  90  deg.  is  the  sun’s 
meridian  altitude.  If  you  turn  the  globe 
about  until  the  index  points  to  any  other  given 
hour,  then  bringing  the  quadrant  of  altitude  to 
cur  the  sun’s  place,  you  will  have  the  sun’s  alti¬ 
tude  at  that  hour ;  and  where  the  quadrant  cuts 
the  horizon,  is  the  sun’s  azimuth  at  the  same 
time.  Thus  May  the  1st,  at  London,  the  sun’s 
meridian  altitude  will  be  531  deg. ;  and  at  10 
o'clock  in  the  morning,  the  sun’s  altitude  will  be 
46  deg.  and  his  azimuth  about  44  deg.  from  the 
south  part  of  the  meridian.  On  the  2d  of  De¬ 
cember,  at  Rome,  at  five  in  the  morning,  the 
altitude  of  Capella  is  41  deg.  58  min.  its  azi¬ 
muth  60  deg.  50  min.  from  N.  to  W. 

382 


OF  THE  GLOBES. 


197 


PROBLEM  XXVI. 

\ 

The  latitude  of  the  place ,  and  the  day  of  the  month 
being  given,  to  find  the  depression  of  the  sun  below 
the  horizon ,  and  the  azimuth,  at  any  hour  of  the 
night . 

Having  rectified  the  globe  for  the  latitude, 
the  zenith,  and  the  sun’s  place,  take  a  point  in 
the  ecliptic  exactly  opposite  to  the  sun’s  place, 
and  find  the  sun’s  altitude  and  azimuth,  as  by 
the  last  problem,  and  these  will  be  the  depres¬ 
sion  and  the  altitude  required. 

Thus  if  the  time  given  be  the  1st  of  Novem¬ 
ber,  at  10  o’clock  at  night,  the  depression  and 
azimuth  will  be  the  same  as  was  found  in  the 
last  problem. 

* 

PROBLEM  XXVII. 

The  latitude ,  the  sunys  place,  and  his  azimuth  being 
given,  to  find  his  altitude ,  and  the  hour . 

Rectify  the  globe  for  the  latitude,  the  zenith, 

i 

and  the  sun’s  place ;  then  put  the  quadrant  of 
altitude  to  the  sun’s  azimuth  in  the  horizon,  and 
turn  the  globe  till  the  sun’s  place  meets  the  edge 
of  the  quadrant ;  then  the  said  edge  will  shew 
the  altitude,  and  the  index  point  to  the  hour. 
Thus,  May  21st,  at  London,  when  the  sun 

383 


198 


DESCRIPTION  AND  USE 


* 

is  due  east,  his  altitude  will  be  about  24  deg. 
and  the  hour  about  VII  in  the  morning ;  and 
when  his  azimuth  is  60  degrees  south-westerly, 
the  altitude  will  be  about  44*  degrees,  and  the 
hour  II ;  in  the  afternoon. 

Thus  the  latitude  and  the  day  being  known, 
and  having  besides  either  the  altitude,  the  azi¬ 
muth,  or  the  hour,  the  other  two  may  be  easily 
found. 

r  r ' 

PROBLEM  XXVIII. 

The  latitude  of  the  place ,  and  the  azimuth  of  the 
sun  or  of  a  star  being  given ,  to  find  the  hour  of 
the  day  or  night . 

* 

Rectify  the  globe  for  the  latitude  and  sun’s 
place,  and  bring  the  quadrant  of  altitude  to  the 
given  azimuth  in  the  horizon  ;  turn  the  globe 
till  the  sun  or  star  comes  to  the  quadrant,  and 
the  index  will  shew  the  time.  November  5,  at 
Gibraltar,  given  the  sun’s  azimuth  50  degrees 
from  the  south  towards  the  east,  the  time  you 
will  find  to  be  half  past  VIII  in  the  morning. 
Given  the  azimuth  of  Vega  at  London,  57  deg. 
from  the  north  towardg  the  east,  February  the 
8th,  the  time  you  will  find  twenty  minutes  past 
II  in  the  morning. 

But  as  it  may  possibly  happen  that  we  may 
see  a  star,  and  would  be  glad  to  know  what  star 
it  is,  or  whether  it  may  not  be  a  new  star,  or  a 

384 


OF  THE  GLOBES. 


199 


comet ;  how  that  may  be  discovered,  will  be  seen 
under  the  following 

PROBLEM  XXIX. 

» 

The  latitude  cf  the  place ,  the  sun  s  place ,  the  hour 
of  the  night ,  and  the  altitude  and  azimuth  of 
any  star  being  given ,  to  find  the  star . 

Rectifying  the  globe  for  the  latitude  of  the  place, 
and  the  sun’s  place  ;  fix  the  quadrant  of  altitude  in 
the  zenith,  and  turn  the  globe  till  the  hour  index 
points  to  the  given  hour,  and  set  the  quadrant  of 
altitude  to  the  given  azimuth  ;  then  the  star  that 
cuts  the  quadrant  in  the  given  altitude,  will  be 
the  star  sought. 

Though  two  stars,  that  have  different  right 
ascensions,  wall  not  come  to  the  meridian  at  the 
same  time,  y£t  it  is  possible  that  in  a  certain  lati¬ 
tude  they  may  come  to  the  same  vertical  circle  at 
the  same  time ;  and  that  consideration  gives  the 
following 

.  1  r  S  / 

PROBLEM  XXX. 

The  latitude  of  the  place ,  the  surfs  place ,  and  two 
stars ,  that  have  the  same  azimuth ,  being  given , 
to  find  the  hour  of  the  night . 

Rectify  the  globe  for  the  latitude,  the  ze¬ 
nith,  and  the  sun’s  place ;  then  turn  the  globe, 

385 


200 


DESCRIPTION  AND  USE 


and  also  the  quadrant  about,  till  both  the  stars 
coincide  with  it’s  edge ;  the  hour  index  will 
shew  the  hour  of  the  night,  and  the  place  where 
the  quadrant  cuts  the  horizon  will  be  the  com¬ 
mon  azimuth  of  both  stars. 

On  the  15th  of  March,  at  London,  the  star 
Betelgeule,  in  the  shoulder  of  Orion,  and  Regel, 
in  the  heel  of  Orion,  were  observed  to  have  the 
same  azimuth ;  on  working  the  problem,  you 
will  find  the  time  to  be  8  hours  47  minutes. 

What  hath  been  observed  above,  of  two  stars 
that  have  the  same  azimuth,  will  hold  good  like¬ 
wise  of  two  stars  that  have  the  same  altitude  ; 
from  whence  we  have  the  following 

PROBLEM  XXXI. 

The  latitude  of  the  place ,  the  surds  place ,  and  two 
stars ,  that  have  the  same  altitude ,  being  given , 
to  find  the  hour  of  the  night . 

Rectify  the  globe  for  the  latitude  of  the  place, 
the  zenith,  and  the  sun’s  place ;  turn  the  globe, 
so  that  the  same  degree  on  the  quadrant  shall 
cut  both  the  stars,  then  the  hour  index  will  shew' 
the  hour  of  the  night. 

In  the  former  propositions,  the  latitude  of 
the  place  is  ‘supposed  to  be  given,  or  known; 
but  as  it  is  frequently  necessary  to  find  the  lati¬ 
tude  of  the  place,  especially  at  sea,  how  this 
may  be  found,  in  a  rude  manner  at  least,  hav- 

386 


OF  THE  GLOBES. 


201 


ing  the  time  given  by  a  good  clocks  or  watch, 
will  be  seen  in  the  following. 

PROBLEM  XXXII. 

The  suns9 s  place ,  the  hour  of  the  night ,  and  two 
stars ,  that  have  the  same  azimuth ,  or  altitude , 
being  given ,  to  find  the  latitude  of  the  place. 

Rectify  the  globe  for  the  sun’s  place,  and 
turn  it  till  the  index  points  to  the  given  hour  of 
the  night  ;  keep  the  globe  from  turning,  and 
move  it  up  and  down  in  the  notches,  till  the  two 
given  stars  have  the  same  azimuth,  or  altitude ; 
then  the  brass  meridian  will  shew  the  height  of 
the  pole,  and  consequently  the  latitude  of  the 
place. 


PROBLEM  XXXII. 

Two  stars  being  given ,  one  on  the  meridian ,  and 
the  other  on  the  east  and  west  part  of  the  horizon , 
to  find  the  latitude  of  the  place. 

Bring  the  star  observed  on  the  meridian  to  the 
meridian  of  the  globe  ;  then  keeping  the  globe 
from  turning  round  it’s  axis,  slide  the  meridian 
up  or  down  in  the  notches,  till  the  other  star  is 
brought  to  the  east  or  west  part  of  the  horizon, 
and  that  elevation  of  the  pole  will  be  the  lati¬ 
tude  of  the  place  sought. 

C  c  387 


202 


DESCRIPTION  and  use 


OBSERVATION. 


£rom  what  hath  been  said,  it-  appears,  that 
of  these  five  things,  1.  the  latitude  of  the  place; 
2.  the  sun’s  place  in  the  ecliptic  ;  3;  the  hour  of 
the  night;  4.  the  common  azimuth  of  two  known 
fixed  stars ;  5.  the  equal  altitude  of  two  known 
fixed  stars  ;  any  three  of  them  being  given,  the 
remaining  two  will  easily  be  found. 

There  are  three  sorts  of  risings  and  settings 
of  the  fixed  stars,  taken  notice  of  by  ancient 
authors,  and  commonly  called  foetial  risings  and 
settings ,  because  mostly  taken  notice  of  by  the 
poets. 

These  are  the  cosmical ,  achronical ,  and  t helia¬ 
cal* 

They  are  to  be  found  in  most  authors  that  treat 
on  the  doctrine  of  the  sphere,  and  are  now  chief¬ 
ly  useful  in  comparing  and  understanding  pas¬ 
sages  in  the  ancient  writers;  such  are  Hesiod,  Vir¬ 
gil,  Columella,  Ovid,  Pliny,  &c.  How  they  are  to 
be  found  by  calculation,  may  be  seen  in  Petavi- 
us’s  Uranologion,  and  Dr.  Gregory’s  Astronomy. 

DEFINITION. 

\  *  V  , 

When  a  star  rises  or  sets  at  sun-risings  it  is  said 
to  rise  or  set  cosmically. 

* 

From  whence  we  shall  have  the  following 

'  t 

*  Costard’s  History  of  Astronomy. 

388 


I 


r 


OF  THE  GLOBES.  208 

_  i 

PROBLEM  XXXIV, 

The  latitude  of  the  place  being  given ,  to  find ,  by 
the  globe ,  of  the  year  when  a  given  star 

rises  or  sets  cosmically . 

Let  the  given  place  be  Rome,  whose  lati¬ 
tude  is  42  deg.  8  min.  north  ;  and  let  the  given 
star  be  the  Lucida  Pleiadum.  Rectify  the  globe 
for  the  latitude  of  the  place  ;  bring  the  star  to 
the  edge  of  the  eastern  horizon,  and  mark  the 
point  of  the  ecliptic  rising  along  with  it ;  that 
will  be  found  to  be  Taurus,  18  deg.  opposite  to 
which,  on  the  horizon,  will  be  found  May  the 
8th.  The  Lucida  Pleiadum,  therefore,  rises  cos¬ 
mically  May  the  8th. 

If  the  globe  continues  rectified  as  before,  and 
the  Lucida  Pleiadum  be  brought  to  the  edge  of 
the  western  horizon,  the  point  of  the  ecliptic, 
which*  is  the  sun’s  place,  then  rising  on  the 
eastern  side  of  the  horizon,  will  be  Scorpio,  29 
deg.  opposite  to  which,  on  the  horizon,  will  be 
found  November  the  2 1st.  The  Lucida  Pleia¬ 
dum,  therefore,  sets  cosmically  November  the  v 
21st. 

In  the  same  manner,  in  the  latitude  of  Lon¬ 
don,  Sirius  will  be  found  to  rise  cosmically  Au¬ 
gust  the  10th,  and  to  set  cosmically  November 
the  loth. 

It  is  of  the  cosmical  setting  of  the  Pleiades, 

389 


i 


204 


DESCRIPTION  AND  USE 


that  Virgil  is  to  be  understood  in  this  line, 

Ante  tibi  Eoa>  Atlanlides  abscondantur ,* 

and  not  of  their  setting  in  the  east ,  as  some  have 
imagined,  where  stars  rise,  but  never  set. 

DEFINITION. 

When  a  star  rises  or  sets  at  sun-setting ,  it  is  said 
to  rise  or  set  achronically. 

Hence,  likewise,  we  have  the  following 

PROBLEM.  XXXV. 

The  latit  ude  of  the  place  being  given ,  to  find  the 
time  of  the  year  when  a  given  star  will  rise  or 
set  achronically . 

'Let  the  given  place  be  Athens,  whose  lati¬ 
tude  is  37  deg.  north,  and  let  the  given  star  be 
Arcturus. 

Rectify  the  globe  for  the  latitude  of  the  place, 
and  bringing  Arcturus  to  the  eastern  side  of  the 
horizon,  mark  the  point  of  the  ecliptic  then  set¬ 
ting  on  the  western  side;  that  will  be  found 
Aries,  12  deg.  opposite  to  which,  on  the  horizon, 
will  be  found  April  the  2d.  Therefore  Arctu¬ 
rus  rises  at  Athens  achronically  April  the  2d. 

It  is  of  this  rising  of  Arcturus  that  Hesiod 
speaks  in  his  Opera  and  Dies.f 

YV  hen  from  the  solstice  sixty  wint'ry  clays 

Their  turns  have  finish’d,  mark,  with  glitt’ring  rays, 

Trom  ocean’s  sacred  flood,  Arcturus  rise, 

Then  first  to  gild  the  dusky  evening  skies. 

*  Georg.  1.  1.  v.  221.  f  Lib.  ii.  ver.  28.>. 

390 


OF  THE  GLOBES. 


*205 


If  the  globe  continues  rectified  to  the  latitude 
of  the  place,  as  before,  and  Arcturus  be  brought 
to  the  western  side  of  the  horizon,  the  point  of 
the  ecliptic  setting  along  with  it  will  be  Sagitta- 
ry,  7  deg.  opposite  to  which,  on  the  horizon, 
will  be  found  November  the  29th.  At  Athens, 
therefore,  Arcturus  sets  achronically  November 
the  29th. 

In  the  same  manner  Aldebaran,  or  the  Bull’s 
eye,  will  be  found  to  rise  achronically  May  the 
22d,  and  to  set  achronically  December  the 
19th. 

DEFINITION. 

t 

When  a  star  first  becomes  visible  in  a  morning , 
after  it  hath  been  so  near  the  sun  as  to  be  hid 
by  the  splendor  of  his  rays ,  it  is  said  to  rise 
HELI  AC  ALLY. 

'  l 

But  for  this  there  is  required  some  certain 
depression  of  the  sun  below  the  horizon,  more 
or  less  according  to  the  magnitude  of  the  star. 
A  star  of  the  first  magnitude  is  commonly  sup¬ 
posed  to  require  that  the  sun  be  depressed  12 
deg.  perpendicularly  below  the  horizon. 

This  being  premised,  we  have  the  follow- 
ing 


i 


391 


206  description  and  use 

I  •  '  V  i 

PROBLEM  XXXVI. 

The  latitude  of  the  place  being  given ,  to  find  the 
time  of  the  year  when  a  given  star  will  rise 
heliacally . 

Let  the  given  place  be  Rome,  whose  latitude 
is  42  deg.  north,  and  let  the  given  star  be  the 
bright  star  in  the  Bull’s  horn. 

Rectify  the  globe  for  the  latitude  of  the 
place,  screw  on  the  brass  quadrant  of  altitude 
in  it’s  zenith,  and  turn  it  to  the  western  side  of 
The  horizon.  Bring  the  star  to  the  eastern  side 
of  the  horizon,  and  mark  what  degree  of  the 
ecliptic  is  cut  by  12  deg.  marked  on  the  quad¬ 
rant  of  altitude  ;  that  will  be  found  to  be  Ca¬ 
pricorn,  3  deg.  the  point  opposite  to  which  is 
Cancer,  3  deg.  and  opposite  to  this  will  be  found 
on  the  horizon,  June  23th.  The  bright  star, 
therefore,  in  the  Bull’s  horn,  in  the  latitude  of 
Rome,  rises  heliacally  June  the  25th. 

These  kinds  of  risings  and  settings  are  not 
only  mentioned  by  the  poets,  but  likewise  by 
the  ancient  physicians  and  historians. 

Thus  Hippocrates,  in  his  book  De  /Ere,  says? 
“  One  ought  to  observe  the  heliacal  risings  and 
settings  of  the  stars,  especially  the  Dog-star ,  and 
Arcturus  ;  likewise  the  cosmical  setting  of  the 
Pleiades .” 

/  * 
And  Polybius,  speaking  of  the  loss  of  the 

892 


OF  THE  GLOBES. 


207 

Roman  fleet,  in  the  first  Punic  war,  says,  cc  It 
was  not  so  much  owing  to  fortune,  as  to  the 
obstinacy  of  the  consuls,  in  not  hearkening  to 
their  pilots,  who  dissuaded  them  from  putting 
to  sea,  at  that  season  of  the  year,  which  was 
between  the  rising  of  Orion  and  the  Dog-star  ; 
it  being  always  dangerous,  and  subject  to 
storms.”* 

t 

DEFINITION. 

When  a  star  is  first  immersed  in  the  evening ,  or 
hid  by  the  sun’s  rays ,  it  is  said  to  set  helia- 

CALLY. 

And  this  again  is  said  to  be,  when  a  star  of 
the  first  magnitude  comes  within  twelve  degrees 
of  the  sun,  reckoned  in  the  perpendicular. 
Hence  again  we  have  the  following 

t  \ 

PROBLEM  XXXVII. 

The  latitude  of  the  place  being  given ,  to  find  the 
time  of  the  year  when  a  given  star  sets  helia - 
cally. 

Let  the  given  place  be  Rome,  in  latitude 
42  deg.  north,  and  let  the  given  star  be  the 
bright  star  in  the  Bull’s  horn.  Rectify  the  globe 
for  the  latitude  of  the  place,  and  bring  the  star 

*  Lib.  i.  p.  5$. 

393 


208  description  and  use 

to  the  edge  of  the  western  horizon  ;  turn  the 
quadrant  of  altitude,  till  12  deg.  cut  the  ecliptic 
on  the  eastern  side  of  the  meridian.  This  will  be 
found  to  be  7  deg.  of  Sagittary,  the  point  oppo¬ 
site  to  which,  in  the  ecliptic,  is  7  deg.  of  Ge¬ 
mini  ;  and  opposite  to  that,  on  the  horizon,  is 
May  the  28th,  the  time  of  the  year  when  that 
sets  heliacally  in  the  latitude  of  Rome. 

OF  THE  CORRESPONDENCE  OF  THE  CELESTIAL  AN1> 

I 

TERRESTRIAL  SPHERES. 

%  #->- 

That  the  reader  may  thoroughly  understand 
what  is  meant  by  the  correspondence  between 
the  two  spheres,  let  him  imagine  the  celestial 
globe  to  be  delineated  upon  glass,  or  any  other 
transparent  matter,  which  shall  invest  or  sur¬ 
round  the  terrestrial  globe,  but  in  such  a  man¬ 
ner,  that  either  may  be  turned  about  upon  the 
poles  of  the  globe,  while  the  other  remains 
fixed  ;  and  suppose  the  first  point  of  Aries,  on 
the  investing  globe,  to  be  placed  on  the  first 
point  of  Aries  on  the  terrestrial  globe,  (which 
point  is  in  the  meridian  of  London)  then  every 
star  in  the  celestial  sphere  will  be  directly  over 
those  places  to  which  it  is  a  correspondent. 
Each  star  will  then  have  the  degree  of  it’s  right 
ascension  directly  upon  the  corresponding  de¬ 
gree  of  terrestrial  longitude  \  their  declination 

894 


OF  THE  GLOBES. 


209 


will  also  be  the  same  with  the  latitude  of  the 
places  to  which  they  answer  ;  or,  in  other  words, 
when  the  declination  of  a  star  is  equal  to  the 
latitude  of  a  place,  such  star,  within  the  space  of 
24  hours,  will  pass  vertically  over  that  place  and 
all  others  that  have  the  same  latitude. 

If  we  conceive  the  celestial  investing  globe  to 
to  be  fixed,  and  the  terrestrial  globe  to  be  gradu¬ 
ally  turned  from  west  to  east,  it  is  clear,  that  as 
the  meridian  of  London  passes  from  one  degree 
to  another  under  the  investing  sphere,  every  star 
in  the  celestial  sphere  becomes  correspondent  to 
another  place  upon  the  earth,  and  so  on,  until 
the  earth  has  completed  one  diurnal  revolution ; 
or  till  all  the  stars,  by  their  apparent  daily  mo¬ 
tion,  have  passed  over  every  meridian  of  the 
terrestrial  globe.  From  this  view  of  the  subject, 
an  amazing  variety,  uniting  in  wonderful  and 
astonishing  harmony,  presents  itself  to  the  atten¬ 
tive  reader ;  and  future  ages  will  find  it  difficult 
to  investigate  the  reasons  that  should  induce  the 
present  race  of  astronomers  to  neglect  a  subject 
so  highly  interesting  to  science,  even  in  a  practi¬ 
cal  view,  but  which  in  theory  would  lead  them 
into  more  sublime  speculations,  than  any  that 
ever  yet  presented  themselves  to  their  minds, 

Dd  395 


210 


DESCRIPTION  AND  USE 


A  GENERAL  DESCRIPTION  OF  THE  PASSAGE  OF  THE 
STAR  MARKED  y  IN  THE  HEAD  OF  THE  CONSTEL¬ 
LATION  DRACO,  OVER  THE  PARALLEL  OF  LONDON. 

The  star  7,  in  the  head  of  the  constellation 
Draco,  having  51  deg,  32  min.  north  declina¬ 
tion,  equal  to  the  latitude  of  London,  is  the  cor¬ 
respondent  star  thereto.  To  find  the  places 
which  it  passes  over,  bring  London  to  the  gradu¬ 
ated  side  of  the  brass  meridian,  and  you  will  find 
that  the  degree  of  the  meridian  over  London,  and 
the  representative  of  the  star,  passes  over  from 
London,  the  road  to  Bristol,  crosses  the  Severn, 
the  Bristol  channel,  the  counties  of  Cork  and 
Kerry  in  Ireland,  the  north  part  of  the  Atlantic 
ocean,  the  streights  of  Belleisle,  New  Britain,  the 
north  part  of  the  province  of  Canada,  New  South 
Wales,  the  southern  part  of  Kamschatka,  thence 
over  different  Tartarian  nations,  several  provinces 
of  Russia,  over  Poland,  part  of  Germany,  the 
southern  part  of  the  United  Provinces,  when, 
crossing  the  sea,  it  arrives  again  at  the  meridian 
of  London. 

When  the  said  star,  or  any  other  star,  is  on 
the  meridian  of  London,  or  any  other  meri¬ 
dian,  all  other  stars,  according  to  their  declina¬ 
tion  and  right  ascension,  and  difference  of  right 
ascension,  (which  answers  to  terrestrial  latitude, 

396 


OF  THE  GLOBES. 


212 


longitude,  and  difference  of  longitude)  will  at  the 
same  time  be  on  such  meridians,  and  vertical  to 
such  places  as  correspond  in  latitude,  longitude, 
and  difference  of  longitude,  with  the  declination, 
kc.  of  the  respective  stars.* 

From  the  stars,  therefore,  thus  considered,  we 
attain  a  copious  field  of  geographical  knowledge, 
and  may  gain  a  clear  idea  of  the  proportionable 
distances  and  real  bearings,  of  remote  empires, 
kingdoms,  and  provinces,from  our  own  zenith,  at 
the  same  instant  of  time  ;  which  may  be  found  in 
the  same  manner  as  we  found  the  place  to  which 
the  sun  was  vertical  at  any  proposed  time. 

Many  instances  of  this  mode  of  attaining  geo¬ 
graphical  knowledge,  may  be  found  in  my 
father’s  treatise  on  the  globes. 


OF  THE  USE  OF  THE  CELESTIAL  GLOBE,  IN  PROBLEMS 
RELATIVE  TO  THE  PLANETS. 


The  situation  of  the  fixed  stars  being  always 
the  same  with  respect  to  one  another,  they  have 
their  proper  places  assigned  to  them  on  the 
globe. 

But  to  the  planets  no  certain  place  can  be  as¬ 
signed,  their  situation  always  varying. 


*  Fairman^s  Geography. 

397 


212 


DESCRIPTION  AND  USE 


I 

That  space  in  the  heavens,  within  the  compass, 
of  which  the  planets  appear,  is  called  the  zodiac. 

The  latitude  of  the  planets  scarce  ever  ex¬ 
ceeding  8  degrees,  the  zodiac  is  said  to  reach 
about  8  degrees  on  each  side  the  ecliptic. 

Upon  the  celestial  globe,  on  each  side  of  the 
ecliptic,  are  drawn  eight  parallel  circles,  at  the 
distance  of  one  degree  from  each  other,  includ¬ 
ing  a  space  of  16  degrees;  these  are  crossed  at 
right  angles,  with  segments  of  great  circles  at 
every  ,5th  degree  of  the  ecliptic ;  by  these,  the 
place  of  a  planet  on  the  globe,  on  any  given  day, 
may  be  ascertained  with  accuracy. 

PROBLEM  XlXXVlII. 

•  » 

To  find  the  place  of  any  planet  upon  the  globe ,  and 
by  that  means  to  find  it's  place  in  the  heavens  : 
also ,  to  find  at  what  hour  any  planet  will  rise  or 
set ,  or  be  on  the  meridian ,  on  any  day  in  the 
year . 

Rectify  the  globe  to  the  latitude  and  sun’s 
place,  then  place  the  planet’s  longitude  and  lati¬ 
tude  in  an  ephemeris,  and  set  the  graduated 
edge  of  the  moveable  meridian  to  the  given 
longitude  in  the  ecliptic,  and  counting  so  ma¬ 
ny  degrees  amongst  the  parallels  in  the  zodiac, 
either  above  or  below  the  ecliptic,  as  her  lati¬ 
tude  is  north  or  south  ;  and  set  the  center  of  the 

398 


OF  THE  GLOBES. 


213 


artificial  sun  to  that  point,  and  the  centre  will 
represent  the  place  of  the  planet  for  that  time. 

Or  fix  the  quadrant  of  altitude  over  the  pole 
of  the  ecliptic,  and  holding  the  globe  fast,  bring 
the  edge  of  the  quadrant  to  cut  the  given  degree 
of  longitude  on  the  ecliptic  ;  then  seek  the  given 
latitude  on  the  quadrant,  and  the  place  under  it 
is  the  point  sought. 

While  the  globe  moves  about  it’s  axis,  this 
point  moving  along  with  it  will  represent  the 
planet’s  motion  in  the  heavens.  If  the  planet 
be  brought  to  the  eastern  side  of  the  horizon,  the 
\  horary  index  will  shew  the  time  of  it’s  rising. 
If  the  artificial  sun  is  above  the  horizon,  the 
• '  planet  will  not  be  visible :  when  the  planet  is 
under  the  strong  brazen  meridian,  the  hour 
index  shews  the  time  it  will  be  on  that  circle  in 
the  heavens  :  when  it  is  at  the  western  edge,  the 
time  of  it’s  setting  will  be  obtained. 

PROBLEM  XXXIX. 

»  /  .  .  .  •  «  / 

To  find  directly  the  planets  which  are  above  the 
horizon  at  sun-set ,  upon  any  given  day  and  lati¬ 
tude . 

Find  the  sun’s  place  for  the  given  day, 
bring  it  to  the  meridian,  set  the  hour  index  to 
XII,  and  elevate  the  pole  for  the  given  lati¬ 
tude  :  then  bring  the  place  of  the  sun  to  the 
western  semicircle  of  the  horizon,  and  observe 

399 


214 


DESCRIPTION  AND  USE 


what  signs  are  in  that  part  of  the  ecliptic  above 
the  horizon,  then  cast  your  eye  upon  the  ephe- 
meris  for  that  month,  and  you  will  at  once  sec 
what  planets  possess  any  of  those  elevated  signs  ; 
for  such  will  be  visible,  and  fit  lor  observation 
on  the  night  of  that  day. 


PROBLEM  XL. 

1  ‘  .  I 

To  find  the  right  ascension ,  declination ,  amplitude , 
azimuth ,  altitude ,  hour  oj  the  nighty  &c.  of  any 
given  planet ,  for  a  day  of  a  month  and  latitude 

given . 

\ 

Rectify  the  globe  for  the  given  latitude  and 
day  of  the  month  ;  then  find  the  planet’s  place, 
as  before  directed,  and  then  the  right  ascension, 
declination,  amplitude,  azimuth,  altitude,  hour, 
&c.  are  all  found,  as  directed  in  the  problems 
for  the  sun ;  there  being  no  difference  in  the 
process,  no  repetition  can  be  necessary. 


OF  THE  USE  OF- THE  CELESTIAL  GLOBE,  IN  PROBLEMS 
RELATIVE  TO  THE  MOON. 

*  X 

From  the  sun  and  planets  we  now  proceed 
to  those  problems  that  concern  the  moon,  the 
brilliant  satellite  of  our  earth,  which  every 
month  enriches  it  with  it’s  presence ;  by  the 
mildness  of  it’s  light  softening  the  darkness  of 

400 


« 


OF  THE  GLOBES.  21 5 

night ;  by  it’s  influence  aftecting  the  tide ;  and 
by  the  variety  of  it’s  aspects,  offering  to  our 
view  some  very  remarkable  phenomena. 

44  Soon  as  the  ev’ning  shades  prevail, 

The  moon  takes  up  the  wondTous  tale  ; 

And  nightly  to  the  listening  earth, 

Repeats  the  story  of  her  birth  : 

Whilst  all  the  stars  that  round  her  burn, 

And  all  the  planets  in  their  turn, 

Confirm  the  tidings  as  they  roll, 

And  spread  the  truth  from  pole  to  pole.” 

As  the  orbit  of  the  moon  is  constantly  vary¬ 
ing  in  its  position,  and  the  place  of  the  node 
always  changing,  as  her  motion  is  even  variable 
in  every  part  of  her  orbit,  the  solutions  of  the 
problems  which  relate  to  her,  are  not  altogether 
so  simple  as  those  which  concern  the  sun. 

The  moon  increases  her  longitude  in  the  eclip¬ 
tic  every  day,  about  13  degrees,  10  minutes,  by 
which  means  she  crosses  the  meridian  of  any 
place  about  50  minutes  later  than  she  did  the 
preceding  day. 

Thus  if  on  any  day  at  noon  her  place  (lon¬ 
gitude)  be  in  the  1 2th  degree  of  Taurus,  it  will 
be  13  deg.  10  min.  more,  or  25  deg.  10  min.  in 
Taurus  on  the  succeeding  noon. 

ft  is  new  moon  when  the  sun  and  moon 

401 


216  * 


DESCRIPTION  AND  USE 


have  the  same  longitude,  or  are  in  or  near  the 
same  point  of  the  ecliptic. 

When  they  have  opposite  longitudes,  or  are 
in  opposite  points  of  the  ecliptic,  it  is  full  moon. 

To  ascertain  the  moon’s  place  with  accuracy, 
we  must  recur  to  an  ephemeris ;  but  as  even  in 
most  ephemerides  the  moon’s  place  is  only  shewn 
at  the  beginning  of  each  day,  or  XII  o’clock  at 
noon,  it  becomes  necessary  to  supply  by  a  table 
this  deficiency,  and  assign  thereby  her  place  for 
any  intermediate  time. 

In  the  nautical  ephemeris,  published  under 
the  authority  of  the  Board  of  Longitude,  we 
have  the  moon’s  place  for  noon  and  midnight, 
with  rules  for  accurately  obtaining  any  interme¬ 
diate  time  ;  but  as  this  ephemeris  may  not  always 
be  at  hand,  we  shall  insert,  from  Mr.  Martin’s 
treatise  on  the  globes,  a  table  for  finding  the 
hourly  motion  of  the  moon.  In  order,  however, 
to  use  this  table,  it  will  be  necessary  first  to  find 
the  quantity  of  the  moon’s  diurnal  motion  in  the 
ecliptic^  for  any  given  day  ;  for  the  quantity  of 
the  moon’s  diurnal  motion  varies  from  about  1 1 
deg.  46  min.  the  least,  to  15  deg.  16  min.  when 
greatest. 

The  following  tables  are  calculated  from 
the  least  of  1 1  deg.  46  min.  to  the  greatest  of 
15  deg.  16  min.  every  column  increasing  10 
minutes ;  upon  the  top  of  the  column  is  the 

402 


OF  THE  GLOBES. 


217 


quantity  of  the  diurnal  motion,  and  on  the  side 
of  the  table  are  the  24*  hours,  by  which  means  it 
will  be  easy  to  find  what  part  of  the  diurnal 
motion  of  the  moon  answers  to  any  given  num¬ 
ber  of  hours. 

Thus  suppose  the  diurnal  motion  to  be  12°  32', 
look  on  the  top  column  for  the  number  nearest 
to  it,  which  you  will  find  to  be  12°  36',  in  the 
sixth  column  ;  and  under  it,  against  9  hours, 
you  will  find  4  deg.  43  min.  which  is  her  motion 
in  the  ecliptic  in  the  space  of  9  hours  for  that 
day.  The  quantity  of  the  diurnal  motion  for 
any  day  is  found  by  taking  the  difference  be« 
tween  it  and  the  preceding  day. 

Thus  let  the  diurnal  motion  for  the  11th  of 
May,  17873  be  required. 

i 

SIGNS.  DEG.  MIN. 

On  the  1 1th  of  May  her  place  was  11  2  35 
On  the  10th  of  May  -  10  19  47 

The  diurnal  motion  sought  ]  2  48 


Ee  40  3 


218  / 


description  and  use 


I  * 

TABLES 

FOR  FINDING  THE  HOURLY  MOTION  OF  THE  MOON,  AND 
THEREBY  HER  TRUE  PLACE  AT  ANY  TIME  OF  THE 
DAY. 

TABLE  I. 


c 

11  46 

11  56 

12. 

12  16 

12  26 

12  36 

12  46 

12  56 

13  6 

13  16 

13  26 

! a 

CO 

• 

d.  m . 

d.  m. 

d.  in. 

d.  in. 

d.  m. 

d.  in. 

d.  m. 

d.  in. 

d.  m. 

d.  m. 

d.  m. 

1 

0  29 

0  30 

0  30 

0  30 

0  31 

0  31 

0  32 

0  32 

0  33 

0  33 

0  34 

2 

0  59 

1  0 

1 

0 

1  1 

1  2 

1  33 

1  4 

1  5 

1  5 

1  6 

1  43 

3 

1  28 

1  20 

1 

31 

1  32 

1  33 

1  35 

1  36 

1  37 

1  38 

1  39 

1  41 

4 

1  58 

1  59 

2 

1 

2  3 

3  4 

2  6 

2  8 

2  9 

2  11 

2  13 

2  14 

5 

2  27 

2  29 

3 

31 

2  34 

2  35 

2  37 

2  40 

2  42 

2  44 

2  46 

2  48 

6 

2  57 

2  59 

3 

1 

3  4 

3  6 

3  9 

3  11 

3  14 

3  16 

3  19 

3  21 

7 

3  26 

3  29 

3 

32 

3  35 

3  38 

3  40 

3  43 

3  46 

3  49 

3  52 

3  55 

8 

3  55 

3  59 

4 

2 

4  6 

4  9 

4  12 

4  15 

4  19 

4  22 

4  25 

4  20 

9 

4  25 

4  28 

4 

32 

4  36 

4  40 

4  43 

4  47 

4  51 

4  55 

4  58 

5  2 

10 

4  54 

4  58 

5 

3 

5  7 

5  11 

5  1 

5  19 

5  23 

5  27 

5  32 

5  56 

11 

5  24 

5  28 

5 

33 

5  37 

5  42 

5  4 

5  51 

5  56 

6  0 

6  3 

6  9 

12 

5  53 

5  53 

6 

3 

6  8 

6  13 

6  18 

6  23 

6  28 

6  33 

6  38 

6  43 

13 

6  22 

6  28 

6  33 

6  39 

6  44 

6  49 

6  55 

7  0 

7  6 

7  11 

7  17 

14 

6  52 

6  58 

7 

3 

7  9 

7  15 

7  21 

7  27 

7  33 

7  38 

7  44 

7  50 

15 

7  21 

7  27 

7 

34 

7  40 

7  46 

7  52 

7  59 

8  5 

8  11 

8  17 

8  24 

15 

7  51 

7  57 

8 

4 

8  11 

8  17 

8  24 

8  31 

8  37 

8  44 

8  51 

8  57 

17 

8  20 

8  27 

8 

34 

8  41 

8  48 

8  55 

9  3 

9  10 

9  17 

9  24 

9  31 

13 

8  49 

8  57 

9 

4 

9  12 

9  19 

9  27 

9  34 

9  42 

9  49 

9  57 

10  4 

19 

9  19 

9  26 

9  35 

9  43 

9  51 

9  58 

10  6 

10  14 

10  22 

10  30 

10  38 

20 

9  48 

9  56 

10 

5 

10  13 

10  21 

10  30 

10  38 

10  47 

10  55 

11  3 

11  12 

21 

10  44 

10  53 

11  1 

11  10 

11  19 

11  27 

11  36 

11  43 

lO  17 

w 

1U  oo 

22 

10  47 

10  56 

11 

6 

11  15 

11  21 

11  33 

11  42 

11  51 

12  0 

12  10 

12  19 

23 

11  17 

11  26 

11 

36. 

11  46 

11  55 

12  4 

12  14 

12  24 

12  33 

12  43 

12  52 

11  46 

11  56 

12 

6 

12  16 

12  26 

12  36 

12  46 

12  56 

13  6 

13  16 

13  26 

404 


/ 


/• 


OF  THE  GLOBES.  2J9 

'  ^  1  t 

:*  s 

**  ■*  * 

TABLE  II. 


— 


K 

O 

13  30 

13  40 

13  50 

14 

6 

14 

10 

14  26 

14 

36 

14  46 

14 

56 

15 

6 

15 

16 

to 

cc 

d.  nu 

d. 

d. 

m. 

d.  m. 

d. 

m. 

m. 

d. 

m. 

d. 

m. 

d. 

tn. 

d. 

m. 

d. 

m. 

d. 

m. 

1 

0 

31 

0  34 

0  35 

0  36 

0  36 

0 

36 

0  36 

0  37 

0  37 

0 

38 

0  38 

2 

1 

8 

1  9 

1  16 

1 

10 

1 

11 

1 

12 

1 

13 

1 

14 

1 

15 

l 

15 

1 

16 

3 

1 

42 

1  42 

1  46 

1 

46 

1 

47 

1 

48 

1 

49 

1 

51 

1 

51 

l 

53 

1 

54 

4 

2 

16 

2  8 

2  19 

2 

21 

2  22 

2 

24 

2  26 

2 

28 

2 

20 

2 

31 

2 

33 

5 

2 

50 

2  52 

2  54 

2 

56 

2  58 

3 

0 

3 

3 

3 

5 

3 

7 

3 

9 

3 

11 

6 

3 

24 

3  26 

3  29 

3 

31 

3 

34 

3 

39 

3 

39 

3 

41 

3 

45 

3 

46 

3 

9 

7 

3 

58 

4  1 

4  4 

4 

7 

4 

10 

4 

10 

4 

15 

4 

18 

4 

21 

4 

24 

4 

7 

8 

4 

» 

32 

4  35 

4  39 

4 

42 

4 

45 

4 

49 

4 

52 

4 

55 

4 

59 

5 

2 

5 

5 

9 

5 

6 

5  10 

5  13 

5 

17 

4 

21 

5 

25 

5 

28 

5 

32 

5 

36 

5 

40 

5 

43 

10 

5 

40 

5  42 

5  48 

5 

52 

5 

57 

6 

1 

6 

5 

6 

9 

6 

13 

6 

17 

6  22 

11 

6 

14 

6  19 

6  23 

6 

28 

6 

32 

6 

37 

6 

41 

6  46 

6 

51 

6 

55 

7 

0 

12 

6  48 

6  53 

6  50 

7 

3 

7 

8 

7 

13 

7 

28 

7 

23 

7 

28 

7 

33 

7  28 

13 

7 

22 

7  27 

7  33 

7 

38 

7 

44 

7  49 

7 

54 

8 

6 

8 

5 

8 

11 

8 

10 

14 

7 

56 

8  0 

8  8 

8 

13 

8 

19 

8 

25 

8 

31 

8 

37 

8 

43 

8 

48 

8 

54 

15 

8 

30 

8  36j 

8  42 

8 

49 

8 

55 

9 

1 

9 

7 

9 

14 

9 

20 

9  26 

9  32 

16 

9 

4 

9  11 

9  17 

9 

21 

9 

12 

9 

37 

9 

44 

9 

51 

9 

57 

10 

4 

10 

11 

17 

9  38 

9  45 

9  52 

9 

59 

10 

20 

10 

13 

10 

20 

10 

28 

10 

33 

10 

42 

10 

49 

18 

10 

12 

10  19  10  27 

10  34 

10 

42 

10  49 

10 

57 

11 

4 

11 

12 

11 

19 

11 

27 

19 

10 

46 

10  54 

11  5 

11 

10 

11 

18 

11 

26 

11 

34 

11 

41 

11 

49 

11 

57 

12 

5 

20 

11 

29 

11  38 

11  37 

11 

24 

11 

8 

12 

2 

12 

10 

12  18 

12 

17 

12  35 

12 

42 

21 

11 

58 

12  3 

12  11 

12 

20 

12 

9 

12 

38 

12  40 

12 

55 

13 

4 

13 

13 

13 

21 

22 

12  28 

12  37 

12  46 

12 

55 

13 

5 

13 

14 

13 

23 

13 

33 

13 

41 

13  50 

13 

50  } 

23 

13 

2 

13  12 

13  21 

13 

31 

13 

43 

13 

59 

13 

59 

14 

9 

14 

10 

14 

28 

14 

38 

24 

13  36 

13  46 

13  56 

14 

6U4 

16 

14  26 

14  36 

14  46 

14  56 

15 

6 

15 

16  I 

40.5 

i 


\  % 


220 


DESC I  RATION  AND  USE 


The  moon’s  path  may'be  represented  on  the 
globe  in  a  very  pleasing  manner,  by  tying  a 
silken  line  over  the  surface  of  the  globe  exactly 
on  the  ecliptic  ;  then  finding,  by  an  ephemeris> 
the  place  of  the  nodes  for  the  given  time,  con¬ 
fine  the  silk  at  these  two  points,  and  at  90  de¬ 
grees  distance  from  them  elevate  the  line  about 
51  deg.  from  the  ecliptic,  and  depress  it  as 
much  on  the  other,  and  it  will  then  represent  the 
lunar  orbit  for  that  day. 

PROBLEM  XLI. 

To  find  the  moon’ s  place  in  the  ecliptic, for  any  given 

hour  of  the  day . 

%  '  s 

First  without  an  ephemeris,  only  knowing  the 
age  of  the  moon,  which  may  be  obtained  from 
every  common  almanack. 

Elevate  the  north  pole  of  the  celestial  globe 
to  90  degrees,  and  then  the  equator  will  be  in 
the  plane  of,  and  coincide  with  the  broad  paper 
circle  ;  bring  the  first  point  of  Aries,  marked  t 
on  the  globe,  to  the  day  of  the  new  moon  on 
the  said  broad  paper  circle,  which  answers  to  the 
sun’s  place  for  that  day ;  and  the  day  of  the 
moon’s  age  will  stand  against  the  sign  and  degree 
of  the  moon’s  mean  place  ;  to  which  place  apply 
a  small  patch  to  represent  the  moon. 

406 


/ 


- ' 

OF  THE  GLOBES.  221 

But  if  you  are  provided  with  an  ephemeris,* 
that  will  give  the  moon’s  latitude  and  place  in 
the  ecliptic  ;  first  note  her  place  in  the  ecliptic 
upon  the  globe,  and  then  counting  so  many  de¬ 
grees  amongst  the  parallels  in  the  zodiac,  either 
above  or  below  the  ecliptic,  as  her  latitude  is 
north  or  south  upon  the  given  day,  and  that  will 
be  the  point  which  represents  the  true  place  of 
the  moon  for  that  time,  to  which  apply  the  arti¬ 
ficial  sun,  or  a  small  patch. 

Thus  on  the  1 1th  of  May,  1787,  she  was  at 
noon  in  2  deg.  35  min.  of  Pisces,  and  her  lati¬ 
tude  was  4  deg.  18  min.;  but  as  her  diurnal 
motion  for  that  day  is  12  48  in  nine  hours,  she 
will  have  passed  over  4  deg.  47  min.  which 
added  to  her  place  at  noon,  gives  7  h.  22  min. 
for  her  place  on  the  11th  of  May,  at,  nine  at 
night. 

»  \ 

PROBLEM  XLII. 

To  find  the  moon’s  declination  for  any  given  day  or 

hour. 

* 

4 

The  place  in  her  orbit  being  found,  by  prob. 
xli,  bring  it  to  the  brazen  meridian  ;  then  the 
arch  of  the  meridian  contained  between  it  and 
the  equinoctial,  will  be  the  declination  sought. 


407 


/ 


DESCRIPTION  and  use 


222 

PROBLEM  XLIII* 

To  find  the  moon's  greatest  and  least  meridian  alti¬ 
tudes  in  any  given  latitude ,  that  of  London  for 
example. 

It  is  evident,  this  can  happen  only  when  the 
ascending  node  of  the  moon  is  in  the  vernal  equi¬ 
nox  ;  for  then  her  greatest  meridian  altitude  will 
be  5  deg.  greater  than  that  of  the  sun,  and  there¬ 
fore  about  67  deg. ;  also  her  least  meridian  alti¬ 
tude  will  be  5  deg.  less  than  that  of  the  sun,  and 
therefore  only  10  deg. :  there  will  therefore  be 
57  deg.  difference  in  the  meridian  altitude  of  the 
moon  ;  whereas  that  of  the  sun  is  but  47  deg. 

N.  B.  When  the  same  ascending  node  is  in 
the  autumnal  equinox,  then  will  her  meridian 
altitude  differ  by  only  37  deg. ;  but  this  pheno¬ 
menon  can  separately  happen  but  once  in  the 
revolution  of  a  node,  or  once  in  the  space  of 
nineteen  years  :  and  it  will  be  a  pleasant  enter¬ 
tainment  to  place  the  silken  line  to  cross  the 
ecliptic  in  the  equinoctial  points  alternately ;  for 
then  the  reason  will  more  evidently  appear,  why 
you  observe  the  moon  sometimes  within  23  deg. 
of  our  zenith,  and  at  other  times  not  more  than 
10  deg.  above  the  horizon,  when  she  is  full 
south. 


408 


I 


OF  THE  GLOBES.  223 

PROBLEM  XL1V. 

To  illustrate *  by  the  globe9  the  phenomenon  oj  the 

harvest  moon . 

About  the  time  of  the  autumnal  equinox, 
when  the  moon  is  at  or  near  the  full,  she  is  ob¬ 
served  to  rise  almost  at  the  same  time  for  several 
nights  together ;  and  this  phenomenon  is  called 
the  harvest  moon . 

This  circumstance,  with  which  farmers  were 
better  acquainted  than  astronomers,  till  within 
these  few  years,  they  gratefully  ascribed  to  the 
goodness  of  God,  not  doubting  that  he  had 
ordered  it  on  purpose  to  give  them  an  immediate 
supply  of  moon-light  after  sun-set,  for  their 
greater  convenience  in  reaping  the  fruits  of  the 
earth. 

In  this  instance  of  the  harvest  moon,  as  in 
many  others  discoverable  by  astronomy,  the 
wisdom  and  beneficence  of  the  Deity  is  conspi¬ 
cuous,  who  really  so  ordered  the  course  of  the 
moon,  as  to  bestow  more  or  less  light  on  all  parts 
*  of  the  earth,  as  their  several  circumstances  or 
seasons  render  it  more  or  less  serviceable.* 

About  the  equator,  where  there  is  no  variety 
of  seasons,  moon-light  is  not  necessary  for  ga¬ 
thering  in  the  produce  of  the  ground ;  and 

*  Ferguson’s  Astronomy. 

409 


224 


description  and  usd 


there  the  moon  rises  about  50  minutes  later 
every  day  or  night  than  on  the  former.  At  con¬ 
siderable  distances  from  the  equator,  where  the 
weather  and  seasons  are  more  uncertain,  the 
autumnal  full  moons  rise  at  sun-set  from  the 
first  to  the  third  quarter.  At  the  poles,  where 
the  sun  is  for  half  a  year  absent,  the  winter  full 
moons  shine  constantly  without  setting,  from  the 
first  to  the  third  quarter. 

But  this  observation  is  still  further  confirmed, 
when  we  consider  that  this  appearance  is  only 
peculiar  with  respect  to  the  full  moon,  from 
which  only  the  farmer  can  derive  any  advantage; 
for  in  every  other  month,  as  well  as  the  three 
autumnal  ones,  the  moon,  for  several  days  to¬ 
gether,  will  vary  the  time  of  it’s  rising  very  little; 
but  then  in  the  autumnal  months  this  happens 
about  the  time  when  the  moon  is  at  the  full ;  in 
the  vernal  months,  about  the  time  of  new  moon  ; 
in  the  winter  months,  about  the  time  of  the  first 
quarter ;  and  in  the  summer  months,  about  the 
time  of  the  last  quarter. 

These  phenomena  depend  upon  the  different 
angles  made  by  the  horizon,  and  different  parts 
of  the  moon’s  orbit,  and  that  the  moon  can  be 
full  but  once  or  twice  in  a  year,  in  those  parts  of 

her  orbit  which  rise  with  the  least  angles. 

•  * 

The  moon’s  motion  is  so  nearly  in  the 

410 


OF  THE  GLOBES. 


22  5 


ecliptic,  that  we  may  consider  her  at  present  as 
moving  in  it. 

The  different  parts  of  the  ecliptic,  on  account 
of  it’s  obliquity  to  the  earth’s  axis,  make  very  dif¬ 
ferent  angles  with  the  horizon  as  they  rise  or  set. 
Those  parts,  or  signs,  which  rise  with  the  small¬ 
est  angles,  set  with  the  greatest,  and  vice  versa • 
In  equal  times,  whenever  this  angle  is  least,  a 
greater  portion  of  the  ecliptic  rises,  than  when 
the  angle  is  larger. 

This  may  be  seen  by  elevating  the  globe  to 
any  considerable  latitude,  and  then  turning  it 
round  it’s  axis  in  the  horizon. 

When  the  moon,  therefore,  is  in  those  signs 
which  rise  or  set  with  the  smallest  angles,  she 
will  rise  or  set  with  the  least  difference  of  time  5 
and  with  the  greatest  difference  in  those  signs 
which  rise  or  set  with  the  greatest  angles. 

Thus  in  the  latitude  of  London,  at  the  time 
of  the  vernal  equinox,  when  the  sun  is  setting 
in  the  western  part  of  the  horizon,  the  ecliptic 
then  makes  an  angle  of  62  deg.  with  the  hori¬ 
zon  ;  but  when  the  sun  is  in  the  autumnal  equi¬ 
nox,  and  setting  in  the  same  western  part  of  the 
horizon,  the  ecliptic  makes  an  angle  but  of  15 
deg.  with  the  horizon ;  all  which  is  evident  by 
a  bare  inspection  of  the  globe  only. 

Again,  according  to  the  greater  or  less  in¬ 
clination  of  the  ecliptic  to  the  horizon,  so  a 
greater  or  less  degree  of  motion  of  the  globe 

Ff41! 


226 


description  and  use 


about  it's  axis  will  be  necessary  to  cause  the 
same  arch  of  the  ecliptic  to  pass  through  the 
horizon  ;  and  consequently  the  time  of  it’s  pas¬ 
sage  will  be  greater  or  less,  in  the  same  propor¬ 
tion  ;  but  this  will  be  best  illustrated  by  an  ex¬ 
ample. 

Therefore,  suppose  the  sun  in  the  vernal 
equinox,  rectify  the  globe  for  the  latitude  of 
London,  and  the  place  of  the  sun ;  then  bring 
the  vernal  equinox,  or  sun’s  place,  to  the  west¬ 
ern  edge  of  the  horizon,  and  the  hour  index 
will  point  precisely  to  VI ;  at  which  time,  we 
will  also  suppose  the  moon  to  be  in  the  au¬ 
tumnal  equinox,  and  consequently  at  full,  and 
rising  exactly  at  the  time  of  sun-set. 

But  on  the  following  day,  the  sun,  being 
advanced  scarcely  one  degree  in  the  ecliptic, 
will  set  again  very  nearly  at  the  same  time  as 
before  ;  but  the  moon  will,  at  a  mean  rate,  in 
the  space  of  one  day,  pass  over  1 3  deg.  in  her 
orbit ;  and  therefore,  when  the  sun  sets  in  the 
evening  after  the  equinox,  the  moon  will  be 
below  the  horizon,  and  the  globe  must  be 
turned  about  till  3  3  deg.  of  Libra  come  up  to 
the  edge  of  the  horizon,  and  then  the  index 
will  point  to  7  h.  16  min,  the  time  of  the  moon’s 
rising,  which  is  an  hour  and  quarter  after  sun¬ 
set  for  dark  night.  The  next  day  following 
there  will  be  cl\  hours,  and  so  on  successively, 
with  an  increase  of  li  hour  dark  night  each 

432 


OF  THE  GLOBES. 


227 


evening  respectively,  at  this  season  of  the  year ; 
all  owing  to  the  very  great  angle  which  the 
ecliptic  makes  with  the  horizon  at  the  time  of 
the  moon’s  rising. 

On  the  other  hand,  suppose  the  sun  in  the 
autumnal  equinox,  or  beginning  of  Libra,  and 
the  moon  opposite  to  it  in  the  vernal  equinox, 
then  the  globe  (rectified  as  before)  being  turned 
about  till  the  sun’s  place  comes  to  the  western 
edge  of  the  horizon,  the  index  will  point  to  VI, 
for  the  time  of  the  setting,  and  the  rising  of 
the  full  moon  on  that  equinoctial  day.  On  the 
following  day,  the  sun  will  set  nearly  at  the 
same  time  ;  but  the  moon  being  advanced  (in 
the  24  hours)  13  deg.  in  the  ecliptic,  the  globe 
must  be  turned  about  till  that  arch  of  the  eclip¬ 
tic  shall  ascend  the  horizon,  which  motion  of 
the  globe  will  be  very  little,  as  the  ecliptic  now 
makes  so  small  an  angle  with  the  horizon,  as 
is  evident  by  the  index,  which  now  points  to 
VI  h.  17.  min.  for  the  time  of  the  moon’s  rising 
dn  the  second  day,  which  is  about  a  quarter  of 
an  hour  after  sun-set.  The  third  day,  the  moon 
wall  rise  within  half  an  hour ;  on  the  fourth, 
within  three  quarters  of  an  hour,  and  so  on ; 
so  that  it  will  be  near  a  week  before  the  nights 
will  be  an  hour  without  illumination ;  and  in 
greater  latitudes  this  difference  will  be  still  great¬ 
er,  as  you  will  easily  find  by  varying  the  case, 
in  the  practice  of  this  celebrated  problem,  on 
the  globe. 


413 


228 


DESCRIPTION  AND  USE 


This  phenomenon  varies  in  different  years ; 
the  moon’s  orbit  being  inclined  to  the  ecliptic 
about  five  degrees,  and  the  line  of  the  nodes 
continually  moving  retrograde,  the  inclination 
of  her  orbit  to  the  equator  will  be  greater  at 
some  seasons  than  it  is  at  others,  which  prevents 
her  hastening  to  the  northward,  or  descending 
southward,  in  each  revolution,  with  an  equal 
pace. 


PROBLEM.  XLV. 

To  find  what  azimuth  the  moon  is  upon  at  any 
place  when  it  is  floods  or  high  water ;  and 
thence  the  high  tide  for  any  day  of  the  moon’t 
age  at  the  same  place . 

Haying  observed  the  hour  and  minute  of 
high  water,  about  the  time  of  new  or  full  moon, 
rectify  the  globe  to  the  latitude  and  sun’s  place  $ 
find  the  moon’s  place  and  latitude  in  an  ephe- 
meris,  to  which  set  the  artificial  moon,*  and 
screw  the  quadrant  of  altitude  in  the  zenith  ; 
turn  the  globe  till  the  horary  index  points  to 
the  time  of  flood,  and  lay  the  quadrant  over  the 
center  of  the  artificial  moon,  and  it  will  cut  the 
horizon  in  the  point  of  the  compass  upon 


*  Or  patch  representing  the  moon, 

414 


OF  THE  GLOBES, 


229 


which  the  moon  was,  and  the  degrees  on  the 
horizon  contained  between  the  strong  brass  me¬ 
ridian  and  the  quadrant,  will  be  the  moon’s  azi¬ 
muth  from  the  south. 


To  find  the  time  of  high  water  at  the  same  place . 

Rectify  the  globe  to  the  latitude  and  zenith, 
find  the  moon’s  place  by  an  ephemeris  for  the 
given  day  of  her  age,  or  day  of  the  month,  and 
set  the  artificial  moon  to  that  place  in  the  zodi¬ 
ac  ;  put  the  quadrant  of  altitude  to  the  azimuth 
before  found,  and  turn  the  globe  till  the  artifi¬ 
cial  moon  is  under  it’s  graduated  edge,  and  the 
horary  index  will  point  to  the  time  of  the  day 
on  which  it  will  be  high  water. 

f 

The  use  of  the  celestial  globe  in  the  solution 

OF  PROBLEMS  ASCERTAINING  THE  PLACES  AND  VISI¬ 
BLE  MOTIONS  OF  ORBITS  OR  COMETS.* 

There  is  another  class  or  species  of  planets, 
which  are  called  comets .  These  move  round 
the  sun  in  regular  and  stated  periods  of  times, 
in  the  same  manner,  and  from  the  same  cause, 
as  the  rest  of  the  planets  do  ;  that  is,  by  a  cen¬ 
tripetal  force,  every  where  decreasing  as  the 

*  Martin’s  Description  and  Use  of  the  Globes. 

415 


2  SO 


..DESCRIPTION  AND  USE 


squares  of  the  distances  increase,  which  is  the 
general  law  of  the  whole  planetary  system.  But 
this  centripetal  force  in  the  comets  being  com¬ 
pounded  with  the  projectile  force,  in  a  very  dif¬ 
ferent  ratio  from  that  which  is  found  in  the 
planets,  causes  their  orbits  to  be  much  more  el¬ 
liptical  than  those  of  the  planets,  which  are  al¬ 
most  circular. 

But  whatever  may  be  the  form  of  a  comet’s 
orbit  in  reality,  their  geocentric  motions,  or 
the  apparent  paths  which  they  describe  in  the 
heavens  among  the  fixed  stars,  will  always  be 
circular,  and  therefore  may  be  shewn  upon  the 
surface  of  a  celestial  globe,  as  well  as  the  mo¬ 
tions  and  places  of  any  of  the  rest  of  the 
planets. 

To  give  an  instance  of  the  cornetary  praxis 
on  the  globe,  we  shall  chuse  that  comet,  for  the 
subject  of  these  problems,  which  made  it’s  ap¬ 
pearance  at  Boston,  in  New  England,  in  the 
months  of  October  and  November*  1758,  in  it’s 
return  to  the  sun  ;  after  which,  it  approached 
so  near  the  sun,  as  to  set  hdiacally ,  or  to  be  lost 
in  it’s  beams  for  some  time  spent  in  passing 
the  perihelion.  Then  afterwards  emerging 
from  the  solar  rays,  it  appeared  retrograde  in 
it’s  course  from  the  sun  towards  the  latter  end 
of  March,  and  so  continued  the  whole  month 
of  April,  and  part  of  May,  in  the  West  Indies, 
particularly  in  Jamaica,  whose  latitude  ren- 

416 


I 


OF  THE  GLOBES.  231 

dered  it  visible  in  those  parts,  when  it  was,  for 
the  greatest  part  of  the  time,  invisible  to  us, 
by  reason  of  it’s  southern  course  through  the 
heavens. 

When  two  observations  can  be  made  of  a 
comet,  it  will  be  very  easy  to  assign  it’s  course, 
or  mark  it  out  upon  the  surface  of  the  celestial 
globe.  These,  with  regard  to  the  above-men¬ 
tioned  comet,  we  have,  and  they  are  sufficient 
for  our  purpose  in  regard  to  the  solution  of 
cometary  problems. 

By  an  observation  made  at  Jamaica  on  the 
31st  of  March,  1759,  at  five  o’clock  in  the 
morning,  the  comet’s  altitude  was  found  to  be 
22  deg.  50  min.  and  it’s  azimuth  71  deg.  south¬ 
east.  From  hence  we  shall  find  its  place  on 
the  surface  of  the  globe  by  the  following  pro¬ 
blem. 

PROBLEM  XL  VI.  • 

To  rectify  the  globe  for  the  latitude  of  the  place 

of  observation  in  Jamaica ,  latitude  17  deg . 

30  min.  and  given  day  of  the  months  viz. 

March  31st. 

Elevate  the  north  pole  to  1 7  deg.  SO  min. 
above  the  horizon,  then  fix  the  quadrant  of  al¬ 
titude  to  the  6ame  degree  in  the  meridian,  or 
zenith  point.  Again,  the  sun’s  place  for  the 
31st  of  March  is  in  10  deg.  34.  min.  which 

417 


DESCRIPTION  AND  USE 


232 

bring  to  the  meridian,  and  set  the  hour  index 
at  XII,  and  the  globe  is  then  rectified  for  the 
place  and  time  of  observation. 

PROBLEM  XLVII. 

♦ 

To  determine  the  place  of  a  comet  on  the  surface  oj 
the  celestial  globe  from  ids  given  altitude ,  azi¬ 
muth,  hour  of  the  day ,  and  latitude  of  the  place . 

The  globe  being  rectified  to  the  given  lati¬ 
tude,  and  day  of  the  month,  turn  it  about  to¬ 
wards  the  east,  till  the  hour  index  points  to  the 
given  time,  viz.  V  o’clock  in  the  morning  ; 
then  bring  the  quadrant  of  altitude  to  intersect 
the  horizon  in  71  deg.  the  given  azimuth  in  the 
south-east  quarter;  then,  under  22  deg.  50  min. 
the  given  altitude,  you  will  find  the  comet’s 
place,  where  you  may  put  a  small  patch  to  re¬ 
present  it 

.  PROBLEM  XLVIIl. 

V 

V 

To  find  the  latitude ,  longitude ,  declination ,  and 
right  ascension  of  the  comets. 

In  the  circles  of  latitude  contained  in  the 
zodiac,  you  will  find  the  latitude  of  the  comet 
to  be  about  30  deg.  30  min.  from  the  ecliptic ; 
the  same  circle  of  latitude  reduces  it’s  place  to 
the  ecliptic  in  26  deg.  30  min.  of  ar,  which  is 

418 


OF  THE  GLOBES. 


233  * 


it’s  longitude  sought.  Then  bring  the  cometary 
1  parch  to  the  brazen  meridian,  and  it's  declination 
will  be  shewn  to  be  9  deg.  15  min.  south.  At 
the  same  time,  it’s  right  aseension  will  be  227 
deg.  30  min. 


) 

P  ROBLEM  XLIX. 


To  shew  the  time  of  the  comet’s  risings  southing , 
setting ,  and  amplitude ,  for  the  day  of  the  obser - 
servation  at  Jamaica . 

Bring  the  place  of  the  comet  into  the  eastern 
semicircle  of  the  horizon,  (the  globe  being  recti¬ 
fied  as  directed)  the  index  will  point  to  III  hours 
15  min.  which  is  the  time  of  it’s  rising  in  the 
morning  at  Jamaica,  the  amplitude  10  deg.  very 
nearly  to  the  south.  The  patch  being  brought 
to  the  meridian,  the  index  points  to  IX  o’clock 
10  min.  for  the  time  of  culminating,  or  being 
south  to  them.  Lastly,  bring  the  patch  to  touch 
the  western  meridian,  and  the  index  will  point 
to  III  in  the  afternoon,  for  the  time  of  the 
comet’s  setting,  with  ten  deg,  of  southern  amplir- 
tude,  of  course. 


G  g  419 


234 


DESCRIPTION  AND  USE 


PROBLEM  L. 

f  -  »  i  * 

From  the  comet's  place  being  given ,  to find  the  time 
of  it's  rising  in  the  horizon  of  London ,  on  the 
3\st  day  of  March ,  1759. 


For  this  purpose,  you  need  only  rectify  the 
globe  for  the  given  latitude  of  London,  and 

bring  the  cometary  patch  to  the  eastern  horizon, 

*  '  - 1 

and  the  index  points  to  III  hours  45  min.  for 
the  time  of  it’s  rising  at  London,  with  about  14 
deg.  of  south  amplitude ;  then  turn  the  patch  to 
the  western  horizon,  and  the  index  points  to  II 
hours  25  minutes,  the  time  of  it’s  setting. 

JN.  B.  From  hence  it  appears,  the  comet  rose 


soon  enough  that  morning  to  have  been  observed 
at  London,  had  the  heavens  been  clear,  and  the 


astronomers  had  been  before-hand  apprized  of 
such  a  phenomenon. 


PROBLEM  LI. 


To  determine  another  place  of  the  same  comet , from 
an  observation  made  at  London  on  the  6th  day- 
of  May ,  at  ten  in  the  evening . 

On  the  6th  day  of  May,  1759,  at  ten  at 
night,  the  place  of  the  comet  was  observed,  and 
it’s  distance  measured  with  a  micrometer,  from 
A  420 


OF  THE  GLOBES. 


235 


two  fixed  stars  marked  v-  and  *  in  the  constella¬ 
tion  called  Hydra ,  and  it’s  altitude  was  found 
to  be  16  deg.  and  it’s  azimuth  37  deg.  south¬ 
west  ;  from  whence  it’s  place  on  the  surface  of 
the  globe,  is  exactly  determined,  as  in  prob. 
xlvii.  and  having  stuck  a  patch  thereon,  you 
will  have  the  two  places  of  the  comet  on  the 
surface  of  the  globe,  for  the  two  distant  days  and 
places  of  observation,  as  required. 

PROBLEM  LII. 

From  two  given  places  of  a  comet ,  to  assign  ids  ap¬ 
parent  path  among  the fixed  stars  in  the  heavens. 

The  two  places  of  the  comet  being  deter* 
mined  by  the  observations  on  the  31st  of 
March,  1758,  and  the  6th  of  May  following, 
and  denoted  by  two  patches  respectively,  you 
must  move  the  globe  up  and  down,  in  the 
notches  of  the  horizon,  till  such  time  as  you 
bring  both  the  patches  to  coincide  with  the 
'  horizon  ;  then  will  the  arch  of  the  horizon  be¬ 
tween  the  two  patches  shew,  upon  the  celestial 
globe,  the  apparent  place  of  the  comet  in  the 
interval  between  the  two  observations,  and  by 
drawing  a  line  with  a  black  lead  pencil  along 
by  the  frame  of  the  horizon,  it*s  path  on  the 
surface  of  the  globe  will  be  delineated,  as  re¬ 
quired.  And  here  it  may  be  observed,  that 

421 


236  DESCRIPTION  AND  USE 

it’s  apparent  path  lay  through  the  following 
southern  constellations,  viz.  the  tail  of  Capri¬ 
corn,  the  tail  of  Piscis  Australis,  by  the  head  of 
Indus,  the  neck  and  body  of  Pavo,  through  the 
neck  of  Apus,  below  Triangulum  Australe, 
above  Musca,  by  the  lowermost  of  the  Crosiers, 
across  the  hind  legs  and  through  the  tail  of 
Centaurus,  from  thence  between  the  two  stars 
in  the  back  of  the  Hydra  before-mentioned ;  af¬ 
ter  this,  it  passed  on  to  Sextans  Uranias,  and 
then  to  the  ecliptic  near  Cor  Leonis,  soon  after 

which  it  totally  disappeared. 

\ 

PROBLEM  LIII. 

t  »  i  - 

To  estimate  the  apparent  velocity  of  a  comety  two 
places  thereof  being  given  by  observation . 

Let  one  place  be  ascertained  near  the  be¬ 
ginning  of  it’s  appearance,  and  the  other  to¬ 
wards  the  end  thereof ;  then  bring  these  two 
places  to  the  horizon,  and  count  the  number 
of  degrees  intersected  between  them,  which  be¬ 
ing  the  space  apparently  described  in  a  given 
time,  will  be  the  velocity  required.  Thus,  in 
the  case  of  the  above-mentioned  comet,  you  will 
find  that  it  described  more  than  150  deg.  in  the 
space  of  36  days,  which  is  more  than  4  deg. 
per  day. 


422 


OF  THE  GLOBES. 


‘237 


l 

PROBLEM  LIV. 


To  represent  the  general  phenomena  of  the  comet , 

for  any  given  latitude . 

Bring  the  visible  path  of  the  comet  to  coin- 
cide  with  the  horizon,  by  which  it  was  drawn, 
and  then  observe  what  degree  of  the  meridian  is 
in  the  north  point  of  the  horizon,  which,  in  the 
case  of  the  foregoing  comet,  will  be  the  23  deg. 
This  will  shew  the  greatest  latitude  in  which  the 
whole  path  can  be  visible  in  any  latitude  less 
than  this,  as  that  of  Jamaica;  where,  for  instance, 
the  most  southern  part  of  the  path  will  be  ele¬ 
vated  more  than  5  deg.  above  the  horizon,  and 
the  comet  visible  through  the  whole  time  of  it’s 
apparition.  But  rectifying  the  globe  for  the 
latitude  of  London,  the  path  of  the  said  comet: 
will  be  for  the  most  part  invisible,  or  below 
the  horizon ;  and  therefore  it  could  not  have 
been  seen  in  our  latitude,  but  at  times  very  near 
the  beginning  and  end  of  it’s  appearance ;  be¬ 
cause,  by  bringing  the  comet’s  path  on  one  part 
to  the  south  point  of  the  horizon,  it  will  imme- 

/  *  l 

diately  appear  in  what  part  the  comet  ceases  to 
be  visible  ;  and  then  the  bringing  the  other  part 
of  the  path  to  the  point,  it  will  appear  in  what 
part  it  will  again  become  visible. 

423 


23 8  DESCRIPTION  AND  USE,  &C, 

Afrer  this  manner  may  the  problems  relating 
to  any  other  comets  be  performed ;  and  thus 
N  the  paths  of  the  several  comets,  which  have 
hitherto  been  observed,  may  be  severally  deli¬ 
neated  on  the  celestial  globe,  and  their  various 
phenomena  in  different  latitudes  be  thereby 
shewn. 


424 


PLATE  X/JI. 


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